Degradable channels, less noisy channels, and quantum statistical morphisms: an equivalence relation

TL;DR

This paper explores the relationships between degradable and less noisy channels in classical and quantum communication, establishing an equivalence relation and providing new insights into their comparative properties.

Contribution

It introduces an equivalence relation between degradable and less noisy channels, unifying classical and quantum cases with new proofs and insights.

Findings

Degradable and less noisy channels are shown to be equivalent under certain conditions.

A new proof for classical noisy channels is provided, highlighting its advantages.

The analysis bridges classical and quantum channel comparison theories.

Abstract

Two partial orderings among communication channels, namely, `being degradable into' and `being less noisy than,' are reconsidered in the light of recent results about statistical comparisons of quantum channels. Though our analysis covers at once both classical and quantum channels, we also provide a separate treatment of classical noisy channels, and show how, in this case, an alternative self-contained proof can be constructed, with its own particular merits with respect to the general result.