Coding Theorems for Quantum Channels

TL;DR

This paper provides a comprehensive overview of quantum channel coding theorems, highlighting recent advances, differences from classical theory, and open problems in quantum information capacity.

Contribution

It offers a self-contained treatment of quantum coding theorems, including recent results on infinite alphabets, constrained inputs, and quantum Gaussian channels.

Findings

Quantum coding theorems have been established for various complex channels.

Recent results include reliability functions for pure state channels.

The paper discusses open problems in quantum information capacity.

Abstract

The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present paper gives a self contained treatment of the subject, following as much in parallel as possible with classical information theory and, on the other side, stressing profound differences of the quantum case. An emphasis is made on recent results, such as general quantum coding theorems including cases of infinite (possibly continuous) alphabets and constrained inputs, reliability function for pure state channels and quantum Gaussian channel. Several still unsolved problems are briefly outlined.