Mutual and coherent informations for infinite-dimensional quantum channels

TL;DR

This paper investigates quantum mutual and coherent information in infinite-dimensional channels, establishing their properties, identities, continuity, and bounds to advance understanding of quantum communication capacities.

Contribution

It introduces appropriate definitions for these quantities in infinite dimensions and proves fundamental identities and bounds, revealing new continuity properties.

Findings

Identified properties of quantum mutual and coherent information in infinite-dimensional channels

Proved identities relating mutual and coherent information of complementary channels

Established an upper bound for coherent information

Abstract

The work is devoted to study of quantum mutual information and coherent information -- the two important characteristics of quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are given and their properties are studied in detail. Basic identities relating quantum mutual information and coherent information of a pair of complementary channels are proved. An unexpected continuity property of quantum mutual information and coherent information following from the above identities is observed. An upper bound for the coherent information is obtained.