Remarks on the classical capacity of quantum channel

TL;DR

This paper provides a direct proof linking the one-shot classical capacity and minimal output entropy for covariant quantum channels, detailing their structure and offering a simple proof for an inequality related to entanglement-assisted capacity.

Contribution

It introduces a direct proof of key capacity relations for covariant quantum channels and clarifies their structural properties.

Findings

Established a relation between one-shot classical capacity and minimal output entropy.

Described the structure of covariant quantum channels in detail.

Provided a simple proof for an inequality involving entanglement-assisted classical capacity.

Abstract

A direct proof of the relation between the one-shot classical capacity and the minimal output entropy for covariant quantum channels is suggested. The structure of covariant channels is described in some detail. A simple proof of a general inequality for entanglement-assisted classical capacity is given.