Convex combinations of CP-divisible Pauli channels that are not semigroups

TL;DR

This paper investigates the non-Markovian properties of convex combinations of Pauli channels, revealing that non-Markovian regions are highly convex and tend to shrink as channels deviate from semigroup structures.

Contribution

It characterizes the geometry of non-Markovian channels formed by convex combinations of Pauli channels, highlighting the counterintuitive behavior of non-Markovianity under channel mixing.

Findings

Non-Markovian regions are highly convex.

The measure of non-Markovianity decreases with deviation from semigroup form.

Convex combinations can produce non-Markovian channels outside of semigroup structures.

Abstract

We study the memory property of the channels obtained by convex combinations of Markovian channels that are not necessarily quantum dynamical semigroups (QDSs). In particular, we characterize the geometry of the region of (non-)Markovian channels obtained by the convex combination of the three Pauli channels, as a function of deviation from the semigroup form in a family of channels. The regions are highly convex, and interestingly, the measure of the non-Markovian region shrinks with greater deviation from the QDS structure for the considered family, underscoring the counterintuitive nature of (non-)Markovianity under channel mixing.