A Measure of Non-Markovianity for Unital Quantum Dynamical Maps

TL;DR

This paper introduces a simple, entropy-based measure to detect non-Markovian behavior in unital quantum dynamical maps, focusing on single-qubit systems and their information back-flow.

Contribution

It proposes a novel, computationally simpler method to identify non-Markovianity in unital quantum maps using von Neumann entropy properties.

Findings

The measure effectively detects non-Markovianity through eigenvalue derivatives.

It simplifies calculations compared to previous methods.

The approach is applicable to single-qubit open quantum systems.

Abstract

One of the most important topics in the study of the dynamics of open quantum system is information exchange between system and environment. Based on the features of a back-flow information from an environment to a system, an approach is provided to detect non-Markovianity for unital dynamical maps. The method takes advantage of non-contractive property of the von Neumann entropy under completely positive and trace preserving unital maps. Accordingly, for the dynamics of a single qubit as an open quantum system, the sign of the time-derivative of the density matrix eigenvalues of the system determines the non-Markovianity of unital quantum dynamical maps. The main characteristics of the measure is to make the corresponding calculations and optimization procedure simpler.