Phase-covariant mixtures of non-unital qubit maps

TL;DR

This paper investigates how convex combinations of phase-covariant, non-unital qubit maps affect their properties, revealing conditions under which unitality is restored and quantum Markovianity is preserved.

Contribution

It provides new insights into the behavior of convex combinations of phase-covariant qubit maps, including conditions for unitality restoration and Markovianity preservation.

Findings

Mixing non-unital channels can restore unitality.

Mixing commutative maps can induce non-commutativity.

Classical uncertainties do not break quantum Markovianity in convex combinations.

Abstract

We analyze convex combinations of non-unital qubit maps that are phase-covariant. In particular, we consider the behavior of maps that combine amplitude damping, inverse amplitude damping, and pure dephasing. We show that mixing non-unital channels can result in restoring the unitality, whereas mixing commutative maps can lead to non-commutativity. For the convex combinations of Markovian semigroups, we prove that classical uncertainties cannot break quantum Markovianity. Moreover, contrary to the Pauli channel case, the semigroup can be recovered only by mixing two other semigroups.