2000 character limit reached
Scalar Curvature of the Quantum Exponential Family for the Transverse-Field Ising Model and the Quantum Phase Transition
Published 25 Dec 2022 in math-ph, cond-mat.stat-mech, and math.MP | (2212.12919v3)
Abstract: Unlike for classical many-body systems, the scalar curvature of the exponential family for quantum many-body systems has been not so investigated, and its physical meaning remains unclear. In this paper, we analytically study the scalar curvature of the space of Gibbs thermal states, belonging to the quantum exponential family, equipped with the Bogoliubov-Kubo-Mori metric for the zero- and one-dimensional transverse-field Ising model at low and high temperatures. We find that these scalar curvatures converge to zero in the high-temperature limit whereas they exponentially diverge approaching zero temperature. This divergence is a consequence of quantumness. Furthermore, if we can reconsider the criticality of the scalar curvatures at zero temperature, they both can be considered to show a critical behavior with an exponent of 1, and this critical exponent is consistent with the quantum-classical correspondence of the Ising model.
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A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. 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Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamics: A Riemannian geometric model. Phys. Rev. A 20(4), 1608–1613 (1979) https://doi.org/10.1103/PhysRevA.20.1608 Crooks [2007] Crooks, G.E.: Measuring Thermodynamic Length. Phys. Rev. Lett. 99(10), 100602 (2007) https://doi.org/10.1103/PhysRevLett.99.100602 Amari and Nagaoka [2000] Amari, S., Nagaoka, H.: Methods of Information Geometry. Oxford University Press, New York (2000) Ruppeiner [1995] Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Crooks, G.E.: Measuring Thermodynamic Length. Phys. Rev. Lett. 99(10), 100602 (2007) https://doi.org/10.1103/PhysRevLett.99.100602 Amari and Nagaoka [2000] Amari, S., Nagaoka, H.: Methods of Information Geometry. Oxford University Press, New York (2000) Ruppeiner [1995] Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Amari, S., Nagaoka, H.: Methods of Information Geometry. Oxford University Press, New York (2000) Ruppeiner [1995] Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. 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D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Amari, S., Nagaoka, H.: Methods of Information Geometry. Oxford University Press, New York (2000) Ruppeiner [1995] Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. 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A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Amari, S., Nagaoka, H.: Methods of Information Geometry. Oxford University Press, New York (2000) Ruppeiner [1995] Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) 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Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. 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A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 67(3), 605–659 (1995) https://doi.org/10.1103/RevModPhys.67.605 Goldenfeld [2018] Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. 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Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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[2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
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A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Goldenfeld, N.: Lectures on Phase Transitions and the Renormalization Group. CRC Press, Boca Raton (2018). https://doi.org/10.1201/9780429493492 Brody and Hook [2008] Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Brody, D.C., Hook, D.W.: Information geometry in vapour–liquid equilibrium. J. Phys. A: Math. and Theor. 42(2), 023001 (2008) https://doi.org/10.1088/1751-8113/42/2/023001 Ruppeiner [2010] Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. 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American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Ruppeiner, G.: Thermodynamic curvature measures interactions. Am. J. Phys. 78(11), 1170–1180 (2010) https://doi.org/10.1119/1.3459936 Ruppeiner [2014] Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ruppeiner, G.: Thermodynamic curvature and black holes. In: Bellucci, S. (ed.) Breaking of Supersymmetry and Ultraviolet Divergences in Extended Supergravity, pp. 179–203. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-03774-5_10 Janyszek and Mrugała [1990] Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and stability of ideal quantum gases. J. Phys. A: Math. Gen. 23(4), 467–476 (1990) https://doi.org/10.1088/0305-4470/23/4/016 Mirza and Mohammadzadeh [2008] Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. 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A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. 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Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. 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E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. 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A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
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Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Mirza, B., Mohammadzadeh, H.: Ruppeiner geometry of anyon gas. Phys. Rev. E 78(2), 021127 (2008) https://doi.org/10.1103/PhysRevE.78.021127 Mirza and Mohammadzadeh [2009] Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Mohammadzadeh, H.: Nonperturbative thermodynamic geometry of anyon gas. Phys Rev E 80(1), 011132 (2009) https://doi.org/10.1103/PhysRevE.80.011132 Provost and Vallee [1980] Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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[2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. 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Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. 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A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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[2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Provost, J.P., Vallee, G.: Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 76(3), 289–301 (1980) https://doi.org/10.1007/BF02193559 Wootters [1981] Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Wootters, W.K.: Statistical distance and Hilbert space. Phys. Rev. D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. 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The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. 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D 23(2), 357–362 (1981) https://doi.org/10.1103/PhysRevD.23.357 Petz [1996] Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. 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[2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. 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Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. 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Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Petz, D.: Monotone metrics on matrix spaces. Linear Algebr. Appl. 244, 81–96 (1996) https://doi.org/10.1016/0024-3795(94)00211-8 Chentsov [1982] Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Chentsov, N.N.: Statistical Decision Rules and Optimal Inference. American Mathematical Society, Providence (1982) Helstrom [1976] Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976) Yuen and Lax [1973] Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Yuen, H., Lax, M.: Multiple-parameter quantum estimation and measurement of nonselfadjoint observables. IEEE Transactions on Information Theory 19(6), 740–750 (1973) https://doi.org/10.1109/TIT.1973.1055103 Petz [1994] Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. 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A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Petz, D.: Geometry of canonical correlation on the state space of a quantum system. J. Math. Phys. 35(2), 780–795 (1994) https://doi.org/10.1063/1.530611 Hayashi [2016] Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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[2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. 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E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. 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[2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hayashi, M.: Quantum Information Theory. Springer, Berlin (2016). https://doi.org/10.1007/978-3-662-49725-8 Kubo et al. [1991] Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. 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Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
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[2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. 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Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Kubo, R., Toda, M., Hashitsume, N.: Statistical Physics II: Nonequilibrium Statistical Mechanics. Springer, Berlin (1991). https://doi.org/10.1007/978-3-642-58244-8 Grasselli and Streater [2001] Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
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Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Grasselli, M.R., Streater, R.F.: ON THE UNIQUENESS OF THE CHENTSOV METRIC IN QUANTUM INFORMATION GEOMETRY. Infinite Dimensional Anal. Quantum Prob. 04(02), 173–182 (2001) https://doi.org/10.1142/S0219025701000462 Uhlmann [1992] Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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[2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. 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[2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. 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Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. 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Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Uhlmann, A.: In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds.) The Metric of Bures and the Geometric Phase, pp. 267–274. Springer, Dordrecht (1992). https://doi.org/10.1007/978-94-011-2801-8_23 Ingarden et al. [1982] Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. 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A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Ingarden, R.S., Janyszek, H., Kossakowski, A., Kawaguchi, T.: Information geometry of quantum statistical systems. Tensor 37, 105–111 (1982) Zanardi et al. [2007] Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. 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A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Zanardi, P., Giorda, P., Cozzini, M.: Information-Theoretic Differential Geometry of Quantum Phase Transitions. Phys. Rev. Lett. 99(10), 100603 (2007) https://doi.org/10.1103/PhysRevLett.99.100603 Dey et al. [2012] Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dey, A., Mahapatra, S., Roy, P., Sarkar, T.: Information geometry and quantum phase transitions in the dicke model. Phys. Rev. E 86, 031137 (2012) https://doi.org/10.1103/PhysRevE.86.031137 Tanaka [2006] Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Tanaka, F.: Kubo–Mori–Bogoliubov Fisher information on the quantum Gaussian model and violation of the scale invariance. J. Phys. A: Math. Gen. 39(45), 14165–14173 (2006) https://doi.org/10.1088/0305-4470/39/45/024 Suzuki [1976] Suzuki, M.: Relationship between d𝑑ditalic_d-dimensional quantal spin systems and (d+1)𝑑1(d+1)( italic_d + 1 )-dimensional Ising systems: Equivalence, critical exponents and systematic approximants of the partition function and spin correlations. Prog. Theor. Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. 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Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. 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Phys. 56(5), 1454–1469 (1976) https://doi.org/10.1143/PTP.56.1454 Hasegawa [1997] Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hasegawa, H.: Exponential and mixture families in quantum statistics: Dual structure and unbiased parameter estimation. Rep. Math. Phys. 39(1), 49–68 (1997) https://doi.org/10.1016/S0034-4877(97)81470-X Janyszek and Mrugała [1989] Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janyszek, H., Mrugała, R.: Riemannian geometry and the thermodynamics of model magnetic systems. Phys. Rev. A 39(12), 6515–6523 (1989) https://doi.org/10.1103/PhysRevA.39.6515 Hübner [1992] Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hübner, M.: Explicit computation of the bures distance for density matrices. Phys. Lett. A 163(4), 239–242 (1992) https://doi.org/10.1016/0375-9601(92)91004-B Zanardi et al. [2007] Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. 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A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. 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[2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Zanardi, P., Venuti, L.C., Giorda, P.: Bures metric over thermal state manifolds and quantum criticality. Phys. Rev. A 76(6), 062318 (2007) https://doi.org/10.1103/PhysRevA.76.062318 Balian [2014] Balian, R.: The entropy-based quantum metric. Entropy 16(7), 3878–3888 (2014) https://doi.org/10.3390/e16073878 Pessoa and Cafaro [2021] Pessoa, P., Cafaro, C.: Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics. Physica A 576, 126061 (2021) https://doi.org/10.1016/j.physa.2021.126061 Pfeuty [1970] Pfeuty, P.: The one-dimensional ising model with a transverse field. Ann. Phys. 57(1), 79–90 (1970) https://doi.org/10.1016/0003-4916(70)90270-8 Suzuki et al. [2012] Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. 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Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
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- Suzuki, S., Inoue, J., Chakrabarti, B.K.: Quantum Ising Phases and Transitions in Transverse Ising Models. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-33039-1 Janke et al. [2002] Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Janke, W., Johnston, D.A., Malmini, R.P.K.C.: Information geometry of the ising model on planar random graphs. Phys. Rev. E 66, 056119 (2002) https://doi.org/10.1103/PhysRevE.66.056119 Janke et al. [2003] Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Janke, W., Johnston, D.A., Kenna, R.: Information geometry of the spherical model. Phys. Rev. E 67(4), 046106 (2003) https://doi.org/10.1103/PhysRevE.67.046106 Mirza and Talaei [2013] Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Mirza, B., Talaei, Z.: Thermodynamic geometry of a kagome ising model in a magnetic field. Phys. Lett. A 377(7), 513–517 (2013) https://doi.org/10.1016/j.physleta.2012.12.030 Hiai et al. [1996] Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Hiai, F., Petz, D., Toth, G.: Curvature in the geometry of canonical correlation. Studia Sci. Math. Hung. 32(1), 235–250 (1996) Dittmann [2000] Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0 Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
- Dittmann, J.: On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric. Linear Algebr. Appl. 315(1), 83–112 (2000) https://doi.org/10.1016/S0024-3795(00)00130-0
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