Family of attainable geometric quantum speed limits
Abstract: We propose a quantum state distance and develop a family of geometrical quantum speed limits (QSLs) for open and closed systems. The QSL time includes an alternative function by which we derive three QSL times with particularly chosen functions. It indicates that two QSL times are exactly the ones presented in Ref. [1] and [2], respectively, and the third one can provide a unified QSL time for both open and closed systems. The three QSL times are attainable for any given initial state in the sense that there exists a dynamics driving the initial state to evolve along the geodesic. We numerically compare the tightness of the three QSL times, which typically promises a tighter QSL time if optimizing the alternative function.
- Z.-Y. Mai and C.-S. Yu, “Tight and attainable quantum speed limit for open systems,” (2023), arXiv:2309.10308 [quant-ph] .
- S. Deffner and S. Campbell, Journal of Physics A: Mathematical and Theoretical 50, 453001 (2017).
- G. C. Hegerfeldt, Phys. Rev. Lett. 111, 260501 (2013).
- S. Campbell and S. Deffner, Phys. Rev. Lett. 118, 100601 (2017).
- J. M. Epstein and K. B. Whaley, Phys. Rev. A 95, 042314 (2017).
- B. Russell and S. Stepney, Phys. Rev. A 90, 012303 (2014a).
- S. Lloyd, Nature 406, 1047 (2000).
- L. Mandelstam and I. Tamm, “The uncertainty relation between energy and time in non-relativistic quantum mechanics,” in Selected Papers, edited by B. M. Bolotovskii, V. Y. Frenkel, and R. Peierls (Springer Berlin Heidelberg, Berlin, Heidelberg, 1991) pp. 115–123.
- N. Margolus and L. B. Levitin, Physica D: Nonlinear Phenomena 120, 188 (1998), proceedings of the Fourth Workshop on Physics and Consumption.
- L. B. Levitin and T. Toffoli, Phys. Rev. Lett. 103, 160502 (2009).
- K. Bhattacharyya, Journal of Physics A: Mathematical and General 16, 2993 (1983).
- G. N. Fleming, Il Nuovo Cimento A 16, 232 (1973).
- N. Hörnedal and O. Sönnerborn, Phys. Rev. Res. 5, 043234 (2023a).
- J. Anandan and Y. Aharonov, Phys. Rev. Lett. 65, 1697 (1990).
- N. Hörnedal and O. Sönnerborn, Phys. Rev. A 108, 052421 (2023b).
- S. Deffner and E. Lutz, Journal of Physics A: Mathematical and Theoretical 46, 335302 (2013a).
- B. Russell and S. Stepney, “A geometrical derivation of a family of quantum speed limit results,” (2014b), arXiv:1410.3209 [quant-ph] .
- X. Cai and Y. Zheng, Phys. Rev. A 95, 052104 (2017).
- S.-x. Wu and C.-s. Yu, Phys. Rev. A 98, 042132 (2018).
- D. Mondal and A. K. Pati, Physics Letters A 380, 1395 (2016).
- O. Andersson and H. Heydari, Journal of Physics A: Mathematical and Theoretical 47, 215301 (2014).
- S. Sun and Y. Zheng, Phys. Rev. Lett. 123, 180403 (2019).
- M. Zwierz, Phys. Rev. A 86, 016101 (2012).
- J. Kupferman and B. Reznik, Phys. Rev. A 78, 042305 (2008).
- M. R. Frey, Quantum Information Processing 15, 3919 (2016).
- S. Deffner and E. Lutz, Phys. Rev. Lett. 111, 010402 (2013b).
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