Mixing doubly stochastic quantum channels with the completely depolarizing channel

TL;DR

This paper proves that mixing doubly stochastic quantum channels with the completely depolarizing channel results in channels that can be expressed as convex combinations of unitary channels, revealing their measure within the space of such channels.

Contribution

It demonstrates that averaging doubly stochastic channels with the depolarizing channel yields convex combinations of unitaries, showing their non-zero measure in the channel space.

Findings

Channels become convex combinations of unitaries after mixing

Non-zero measure of such channels within doubly stochastic channels

Provides a structural insight into quantum channel convexity

Abstract

It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of channels expressible as convex combinations of unitary channels has non-zero Borel measure within the space of doubly stochastic channels.