Generalized trace distance approach to quantum non-Markovianity and detection of initial correlations

TL;DR

This paper generalizes a measure of quantum non-Markovianity using trace norm of Helstrom matrices, demonstrating its consistency with information flow interpretation and improving detection of initial correlations.

Contribution

It introduces a generalized trace distance approach for quantum non-Markovianity, linking it to information flow and optimizing local detection strategies for quantum correlations.

Findings

The generalized measure aligns with the original interpretation of information flow.

A bound on external information growth is established.

The optimality of a previous detection strategy is demonstrated.

Abstract

A measure of quantum non-Markovianity for an open system dynamics, based on revivals of the distinguishability between system states, has been introduced in the literature using the trace distance as quantifier for distinguishability. Recently it has been suggested to use as measure for the distinguishability of quantum states the trace norm of Helstrom matrices, given by weighted differences of statistical operators. Here we show that this new approach, which generalizes the original one, is consistent with the interpretation of information flow between the system and its environment associated to the original definition. To this aim we prove a bound on the growth of the external information, that is information which cannot be accessed by performing measurements on the system only, as quantified by means of the Helstrom matrix. We further demonstrate by means of example that it is of relevance in generalizing schemes for the local detection of initial correlations based on the increase of internal information. Finally we exploit this viewpoint to show the optimality of a previously introduced strategy for the local detection of quantum correlations.