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

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.