Holevo skew divergence for the characterization of information backflow

TL;DR

This paper introduces a framework using Holevo skew divergence to characterize information backflow in quantum systems, linking various non-Markovianity measures and applying the theory to specific physical models.

Contribution

It extends the mathematical framework of non-Markovianity characterization by incorporating Holevo quantity as a key divergence measure and relates different quantifiers within this formalism.

Findings

Established the Holevo skew divergence as a tool for non-Markovianity analysis

Connected multiple non-Markovianity quantifiers within a unified framework

Applied the theory to two physical models with exact evaluations

Abstract

The interpretation of non-Markovian effects as due to the information exchange between an open quantum system and its environment has been recently formulated in terms of properly regularized entropic quantities, as their revivals in time can be upper bounded by means of quantities describing the storage of information outside the open system [Phys. Rev. Lett. 127, 030401 (2021)]. Here, we elaborate on the wider mathematical framework of the theory, specifying the key properties that allow us to associate distinguishability quantifiers with the information flow from and towards the open system. We point to the Holevo quantity as a distinguished quantum divergence to which the formalism can be applied, and we show how several distinct quantifiers of non-Markovianity can be related to each other within this general framework. Finally, we apply our analysis to two relevant physical models in which an exact evaluation of all quantities can be performed.