Quantum Dynamical Entropy and Dissipative Information Flows

TL;DR

This paper extends the ALF quantum dynamical entropy to open systems, providing a new measure of environmental information back-flow, with exact results for a qubit-spin chain model.

Contribution

It introduces an open-system ALF entropy that captures environmental information flow, surpassing previous reduced-dynamics-based measures.

Findings

Exact expression for open-system ALF entropy in a qubit-spin chain model

Demonstrates how environmental information flow relates to entropy production

Shows reversibility corresponds to zero entropy production in specific cases

Abstract

The Alicki-Lindblad-Fannes dynamical (ALF) entropy measures the rate at which new information is gathered about a quantum system by inspecting its long-time evolution. We propose an extension of the ALF entropy to open quantum dynamics as a measure of back-flow of information from the environment. Such a proposal is stronger than the existing ones based only on the open system reduced dynamics. In the case of a qubit collisionally coupled to a classical spin chain, we obtain an exact expression for the $\textit{open-system ALF entropy}$ explicitly depending on the environment correlations. An extreme case shows how the information flow from environment to system corresponds to vanishing entropy production as for reversible finite quantum systems.