Potential output purity of completely positive maps

TL;DR

This paper introduces the concept of potential output purity for completely positive maps, establishes bounds for it, and applies these results to analyze the properties of certain quantum channels and their associated constants.

Contribution

It generalizes the notion of output purity, derives upper bounds for potential purity, and applies these bounds to quantum channel analysis and constants.

Findings

Potential purity does not exceed standard output purity for several classes of maps.

An upper bound for potential output purity is derived.

Potential purity is used to bound the logarithmic Sobolev constant of depolarizing channels.

Abstract

The notion of potential output purity of a completely positive map is introduced as a generalization of the regularized output purity. An upper bound is derived for this quantity, and for several classes of maps (including CQ, QC and Hadamard channels) it is shown that potential purity does not exceed the standard output purity. As an application the potential purity is used to bound the logarithmic Sobolev constant of a product of depolarizing channel semigroups.