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Physical Review A

Comment on “Modified quantum-speed-limit bounds for open quantum dynamics in quantum channels”

Nicolás Mirkin, Fabricio Toscano, Diego A. Wisniacki

Published Apr 6, 2018• 2 citations
Publisher

Abstract

In a recent paper [Phys. Rev. A 95, 052118 (2017)], the authors claim that our criticism, in Phys. Rev. A 94, 052125 (2016), to some quantum speed limit bounds for open quantum dynamics that appeared recently in literature are invalid. According to the authors, the problem with our analysis would be generated by an artifact of the finite-precision numerical calculations. We analytically show here that it is not possible to have any inconsistency associated with the numerical precision of calculations. Therefore, our criticism of the quantum speed limit bounds continues to be valid.

DOI
10.1103/physreva.97.046101

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The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.

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In a recent paper [Phys. Rev. A 95, 052118 (2017)], the authors claim that our criticism, in Phys. Rev. A 94, 052125 (2016), to some quantum speed limit bounds for open quantum dynamics that appeared recently in literature are invalid. According to the authors, the problem with our analysis would be generated by an artifact of the finite-precision numerical calculations. We analytically show here that it is not possible to have any inconsistency associated with the numerical precision of calculations. Therefore, our criticism of the quantum speed limit bounds continues to be valid.
The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.
The minimal evolution time between two distinguishable states is of fundamental interest in quantum physics. Very recently Mirkin et al. [Phys. Rev. A 94, 052125 (2016)] argued that some of the most common quantum-speed-limit (QSL) bounds which depend on the actual evolution time do not cleave to the essence of the QSL theory as they grow indefinitely but the final state is reached at a finite time in a damped Jaynes-Cummings model. In this paper, we thoroughly study this puzzling phenomenon. We find the inconsistent estimates will happen if and only if the limit of resolution of a calculation program is achieved, through which we propose that the nature of the inconsistency is not a violation of the essence of the QSL theory but an illusion caused by the finite precision in numerical simulations. We also present a generic method to overcome the inconsistent estimates and confirm its effectiveness in both amplitude-damping and phase-damping channels. Additionally, we show special cases which may restrict the QSL bound defined by ``quantumness''.
Recently, Jones and Kok [Jones and Kok, Phys. Rev. A 82, 022107 (2010)] presented alternative geometric derivations of the Mandelstam-Tamm [Mandelstam and Tamm, J. Phys. (USSR) 9, 249 (1945)] and Margolus-Levitin [Margolus and Levitin, Phys. D 120, 188 (1998)] inequalities for the quantum speed of dynamical evolution. The Margolus-Levitin inequality followed from an upper bound on the rate of change of the statistical distance between two arbitrary pure quantum states. We show that the derivation of this bound is incorrect. Subsequently, we provide two upper bounds on the rate of change of the statistical distance, expressed in terms of the standard deviation of the generator KKK and its expectation value above the ground state. The bounds lead to the Mandelstam-Tamm inequality and a quantum speed limit which is only slightly weaker than the Margolus-Levitin inequality.