Geometrical characterization of non-Markovianity

TL;DR

This paper introduces a new geometric method to quantify non-Markovian behavior in quantum systems, applicable to both discrete and continuous-variable systems, and demonstrates its effectiveness through canonical examples.

Contribution

It presents a novel geometric tool for quantifying non-Markovianity, extending to general N-level and Gaussian continuous-variable systems.

Findings

The tool measures changes in the volume of accessible states.

It aligns qualitatively with existing non-Markovianity measures.

Successfully applied to canonical quantum dynamics examples.

Abstract

We introduce a new tool for the quantitative characterisation of the departure form Markovianity of a given dynamical process. Our tool can be applied to a generic $N$-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its prediticve power by tackling a few canonical examples.