Fundamental limits on quantum dynamics based on entropy change

TL;DR

This paper investigates the fundamental limits of entropy change in quantum dynamics, deriving bounds that serve as witnesses for non-unitality and memory effects, thereby advancing the understanding of quantum evolution processes.

Contribution

It introduces a lower bound on the rate of entropy change for quantum systems, providing new tools to characterize non-unital and memory effects in quantum dynamics.

Findings

Derived a lower limit on entropy change rate for memoryless quantum dynamics.

Established entropy change bounds as witnesses for non-unitality.

Proposed measures for non-unitarity based on entropy change bounds.

Abstract

It is well known in the realm of quantum mechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde~[Phys.~Rev.~A~93(6),~062314~(2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characterize quantum dynamics. In particular, we derive a lower limit on the rate of entropy change for memoryless quantum dynamics, and we argue that it provides a witness of non-unitality. This limit on the rate of entropy change leads to definitions of several witnesses for testing memory effects in quantum dynamics. Furthermore, from the aforementioned lower bound on entropy change, we obtain a measure of non-unitarity for unital evolutions.