Characterization of P-divisibility in two-level open quantum systems

TL;DR

This paper provides a comprehensive analysis of P-divisibility in two-level quantum systems, establishing necessary and sufficient conditions, proving equivalences among different characterizations, and exploring implications for non-Markovianity measures.

Contribution

It introduces new inequalities for P-divisibility, proves equivalences among existing characterizations, and applies these results to a qubit-bosonic mode interaction.

Findings

Derived inequalities for P-divisibility conditions

Proved equivalence of multiple P-divisibility characterizations

Analyzed qubit dynamics interacting with a bosonic mode

Abstract

We study different characterizations of P-divisibility in two-level open quantum systems whose dynamics are governed by a time-local master equation with time-dependent relaxation rates. Necessary and sufficient conditions for the P-divisibility of the dynamical map are given in terms of inequalities on such relaxation rates. The equivalence between several P-divisibility characterizations existing in the literature is explicitly proven. The connection to the Breuer-Laine-Piilo measure of non-Markovianity is also established. As an application of such characterizations, we study the open dynamics of a qubit interacting with a bosonic mode. More precisely, we characterize the properties of the local map on the qubit generated by its interaction with the bosonic mode, playing the role of an extremely reduced bath. Interesting observations are made, opening perspectives for a deeper physical understanding of CP-divisibility, P-divisibility, and BLP measure.