Fluctuation and dissipation in memoryless open quantum evolutions

TL;DR

This paper explores the relationship between entropy rates and quantum Fisher information in memoryless open quantum systems, deriving a quantum fluctuation-dissipation relation and analyzing stationarity in quantum Gaussian channels.

Contribution

It introduces a novel decomposition of the generator of quantum dynamical semigroups, linking entropy rate with quantum Fisher information and extending classical fluctuation-dissipation concepts to quantum channels.

Findings

Derived a quantum de Bruijn identity for Gaussian channels.

Established a relation between entropy rate and quantum Fisher information.

Analyzed conditions for stationarity in quantum dynamical semigroups.

Abstract

Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum dynamical semigroup, we find a decomposition of the infinitesimal generator of the dynamics, that allows to relate the von Neumann entropy rate with the divergence-based quantum Fisher information, at any time. Applied to quantum Gaussian channels that are dynamical semigroups, our decomposition leads to the quantum analog of the generalized classical de Bruijn identity, thus expressing the quantum fluctuation-dissipation relation in that kind of channels. Finally, from this perspective, we analyze how stationarity arises.