Quantifying non-Markovianity via conditional mutual information

TL;DR

This paper introduces measures of quantum non-Markovianity based on conditional mutual information, linking it to recovery maps, Markov chains, and environment correlations, providing new insights into quantum memory effects.

Contribution

It develops a multipartite approach to quantify quantum non-Markovianity using conditional mutual information, highlighting the role of environment correlations in nonlocal memory effects.

Findings

Conditional mutual information relates to recovery maps and Markov chains

Correlated environments are necessary for nonlocal memory effects

Leaked information can be back flowed in quantum systems

Abstract

In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change of distinguishability. We study along the way the properties of leaked information which is the conditional mutual information that can be back flowed, and we use this leaked information to show that the correlated environment is necessary for nonlocal memory effect.