Comparison of Noisy Channels and Reverse Data-Processing Theorems

TL;DR

This paper investigates how different noisy communication channels can be compared in terms of their effectiveness using statistical decision theory, establishing an equivalence relation across classical and quantum channels.

Contribution

It introduces a unified framework for comparing classical and quantum noisy channels through an equivalence relation, advancing the theoretical understanding of channel ordering.

Findings

Established an equivalence relation for classical channels.

Extended the relation to quantum channels with classical encoding.

Extended the relation to quantum channels with quantum encoding.

Abstract

This paper considers the comparison of noisy channels from the viewpoint of statistical decision theory. Various orderings are discussed, all formalizing the idea that one channel is "better" than another for information transmission. The main result is an equivalence relation that is proved for classical channels, quantum channels with classical encoding, and quantum channels with quantum encoding.