Probing the degree of non-Markovianity for independent and common environments

TL;DR

This paper analyzes how the degree of non-Markovianity in open quantum systems varies with different environmental interactions and measures, revealing complex dependencies on system size and environmental type.

Contribution

It compares two measures of non-Markovianity and explores their behavior in systems with independent and common environments, highlighting non-trivial dependencies.

Findings

Non-Markovianity depends on the quantum process and environment type.

Degree of non-Markovianity generally increases with qubits in independent environments.

In common environments, non-Markovianity can increase or decrease based on quantum process properties.

Abstract

We study the non-Markovianity of the dynamics of open quantum systems focusing on the cases of independent and common environmental interactions. We investigate the degree of non-Markovianity quantified by two distinct measures proposed by Luo, Fu and Song (LFS) and Breuer, Laine and Pillo (BLP). We show that the amount of non-Markovianity, for a single and a pair of qubits, depends on the quantum process, the proposed measure and whether the environmental interaction is collective or independent. In particular, we demonstrate that while the degree of non-Markovianity generally increases with the number of the qubits in the system for independent environments, the same behavior is not always observed for common environments. In the latter case, our analysis suggests that the amount of non-Markovianity could increase or decrease depending on the properties of the considered quantum process.