2000 character limit reached
Boundary effect and correlations in fermionic Gaussian states
Published 15 Apr 2024 in quant-ph | (2404.09428v2)
Abstract: The effect of boundaries on the bulk properties of quantum many-body systems is an intriguing subject of study. One can define a boundary effect function, which quantifies the change in the ground state as a function of the distance from the boundary. This function serves as an upper bound for the correlation functions and the entanglement entropies in the thermodynamic limit. Here, we perform numerical analyses of the boundary effect function for one-dimensional free-fermion models. We find that the upper bound established by the boundary effect fuction is tight for the examined systems, providing a deep insight into how correlations and entanglement are developed in the ground state as the system size grows. As a by-product, we derive a general fidelity formula for fermionic Gaussian states in a self-contained manner, rendering the formula easier to apprehend.
- Hatsugai, Y.: Chern number and edge states in the integer quantum Hall effect. Physical Review Letters 71, 3697–3700 (1993) Lu and Vishwanath [2012] Lu, Y.-M., Vishwanath, A.: Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach. Physical Review B 86, 125119 (2012) Eisert et al. [2010] Eisert, J., Cramer, M., Plenio, M.B.: Colloquium: Area laws for the entanglement entropy. Reviews of Modern Physics 82, 277 (2010) Cho [2014] Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Lu, Y.-M., Vishwanath, A.: Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach. Physical Review B 86, 125119 (2012) Eisert et al. [2010] Eisert, J., Cramer, M., Plenio, M.B.: Colloquium: Area laws for the entanglement entropy. Reviews of Modern Physics 82, 277 (2010) Cho [2014] Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Eisert, J., Cramer, M., Plenio, M.B.: Colloquium: Area laws for the entanglement entropy. Reviews of Modern Physics 82, 277 (2010) Cho [2014] Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Lu, Y.-M., Vishwanath, A.: Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach. Physical Review B 86, 125119 (2012) Eisert et al. [2010] Eisert, J., Cramer, M., Plenio, M.B.: Colloquium: Area laws for the entanglement entropy. Reviews of Modern Physics 82, 277 (2010) Cho [2014] Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Eisert, J., Cramer, M., Plenio, M.B.: Colloquium: Area laws for the entanglement entropy. Reviews of Modern Physics 82, 277 (2010) Cho [2014] Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Eisert, J., Cramer, M., Plenio, M.B.: Colloquium: Area laws for the entanglement entropy. Reviews of Modern Physics 82, 277 (2010) Cho [2014] Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Cho, J.: Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems. Physical Review Letters 113, 197204 (2014) Cho [2015] Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Cho, J.: Correlations in quantum spin systems from the boundary effect. New Journal of Physics 17, 053021 (2015) Fredenhagen [1985] Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Fredenhagen, K.: A remark on the cluster theorem. Communications in Mathematical Physics 97, 461–463 (1985) Hastings and Koma [2006] Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Hastings, M.B., Koma, T.: Spectral Gap and Exponential Decay of Correlations. Communications in Mathematical Physics 265, 781–804 (2006) Nachtergaele and Sims [2006] Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Nachtergaele, B., Sims, R.: Lieb-Robinson Bounds and the Exponential Clustering Theorem. Communications in Mathematical Physics 265, 119–130 (2006) Hastings [2007] Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Hastings, M.B.: An area law for one-dimensional quantum systems. Journal of Statistical Mechanics: Theory and Experiment 2007, 08024 (2007) Brandão and Horodecki [2013] Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Brandão, F.G.S.L., Horodecki, M.: An area law for entanglement from exponential decay of correlations. Nature Physics 9, 721–726 (2013) Cho [2018] Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Cho, J.: Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations. Physical Review X 8, 031009 (2018) Swingle and Wang [2019] Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Swingle, B., Wang, Y.: Recovery Map for Fermionic Gaussian Channels. Journal of Mathematical Physics 60, 072202 (2019) Bravyi [2005] Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Bravyi, S.: Lagrangian representation for fermionic linear optics. Quantum Information and Computation 5, 216–238 (2005) Gaudin [1960] Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Gaudin, M.: Une démonstration simplifiée du théorème de wick en mécanique statistique. Nuclear Physics 15, 89–91 (1960) Banchi et al. [2014] Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Banchi, L., Giorda, P., Zanardi, P.: Quantum information-geometry of dissipative quantum phase transitions. Physical Review E 89, 022102 (2014) Choi [1975] Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra and its Applications 10, 285–290 (1975) Nielsen and Chuang [2011] Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011) Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
- Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, Cambridge ; New York (2011)
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