Notes on entropic characteristics of quantum channels

TL;DR

This paper explores entropic measures of quantum channels, establishing bounds and properties of generalized entropies like the $q$-entropy and $(q,s)$-entropy exchange, to better understand information transmission in noisy quantum environments.

Contribution

It introduces bounds and concavity properties of generalized entropies for quantum channels, extending traditional von Neumann entropy analysis.

Findings

The $q$-average output entropy is bounded by the $q$-entropy of the input.

Concavity properties of the $(q,s)$-entropy exchange are analyzed.

Upper bounds on the $(q,s)$-entropy exchange are derived.

Abstract

One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss few channel characteristics expressed by means of generalized entropies. Such characteristics can often be dealt in line with more usual treatment based on the von Neumann entropies. For any channel, we show that the $q$-average output entropy of degree $q\geq1$ is bounded from above by the $q$-entropy of the input density matrix. Concavity properties of the $(q,s)$-entropy exchange are considered. Fano type quantum bounds on the $(q,s)$-entropy exchange are derived. We also give upper bounds on the map $(q,s)$-entropies in terms of the output entropy, corresponding to the completely mixed input.