Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps

TL;DR

This paper investigates the conditions under which mixtures of noninvertible Pauli dynamical maps exhibit non-Markovian behavior, providing criteria and examples for understanding their divisibility and non-Markovianity properties.

Contribution

It establishes necessary and sufficient conditions for Pauli maps to satisfy divisibility criteria and explores how non-Markovianity properties are affected in their convex combinations.

Findings

Derived criteria for non-Markovianity in Pauli maps.

Identified conditions for divisibility in noninvertible dynamical maps.

Proposed a time-local generator with infinite decoherence rates for P-divisible maps.

Abstract

We analyze the connections between the non-Markovianity degree of the most general phase-damping qubit maps and their legitimate mixtures. Using the results for image non-increasing dynamical maps, we formulate the necessary and sufficient conditions for the Pauli maps to satisfy specific divisibility criteria. Next, we examine how the non-Markovianity properties for (in general noninvertible) Pauli dynamical maps influence the properties of their convex combinations. Our results are illustrated with instructive examples. For P-divisible maps, we propose a legitimate time-local generator whose all decoherence rates are temporarily infinite.