Singularities, mixing and non-Markovianity of Pauli dynamical maps

TL;DR

This paper investigates whether mixing non-singular qubit Pauli channels can produce singularities, concluding it is not possible, but mixing singular channels can eliminate singularities, with implications for quantum channel realization.

Contribution

It demonstrates that mixing non-singular channels cannot produce singularities, and explores how mixing singular channels affects channel singularities and non-Markovianity.

Findings

Mixing non-singular channels cannot produce singularities.

Mixing singular channels can eliminate singularities.

Results restrict experimental realization of non-invertible channels.

Abstract

Quantum non-Markovianity of channels can be produced by mixing Markovian channels, as observed recently by various authors. We consider an analogous question of whether singularities of the channel can be produced by mixing non-singular channels, i.e., ones that lack them. Here we answer the question in the negative in the context of qubit Pauli channels. On the other hand, mixing channels with a singularity can lead to the elimination of singularities in the resultant channel. We distinguish between two types of singular channels, which lead under mixing to broadly quite different properties of the singularity in the resultant channel. The connection to non-Markovianity (in the sense of completely positive indivisibility) is pointed out. These results impose nontrivial restrictions on the experimental realization of non-invertible quantum channels by a process of channel mixing.