On measures of non-Markovianity: divisibility vs. backflow of information

TL;DR

This paper compares two measures of quantum non-Markovianity, revealing they can disagree and exploring their relationships through a toy model and potential generalizations.

Contribution

It provides a detailed analysis of two non-Markovianity measures, highlighting their differences and proposing possible generalizations.

Findings

The two measures can yield different results for the same quantum process.

A toy model demonstrates the disagreement between the measures.

Discussion of potential extensions and relations between measures.

Abstract

We analyze two recently proposed measures of non-Markovianity: one based on the concept of divisibility of the dynamical map and the other one based on distinguishability of quantum states. We provide a toy model to show that these two measures need not agree. In addition, we discuss possible generalizations and intricate relations between these measures.