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.

Mixing non-unital qubit maps can restore unitality, while mixing commutative maps can lead to non-commutativity, and classical uncertainties cannot break quantum Markovianity.

Phase-covariant mixtures of non-unital qubit maps

Key Takeaway: Mixing non-unital qubit maps can restore unitality, while mixing commutative maps can lead to non-commutativity, and classical uncertainties cannot break quantum Markovianity.