Coding Theorems of Quantum Information Theory

TL;DR

This paper establishes coding theorems and strong converses for quantum communication channels and sources, introduces new proofs for classical information transmission, and explores multi-user quantum systems and quantum source compression.

Contribution

It provides new proofs of coding theorems and the Holevo bound, and determines the capacity region for quantum multiple access channels.

Findings

Proved strong converse for quantum sources and channels

Determined capacity region for quantum multiple access channel

Introduced a framework for quantum source compression and entropy calculus

Abstract

Coding theorems and (strong) converses for memoryless quantum communication channels and quantum sources are proved: for the quantum source the coding theorem is reviewed, and the strong converse proven. For classical information transmission via quantum channels we give a new proof of the coding theorem, and prove the strong converse, even under the extended model of nonstationary channels. As a by-product we obtain a new proof of the famous Holevo bound. Then multi-user systems are investigated, and the capacity region for the quantum multiple access channel is determined. The last chapter contains a preliminary discussion of some models of compression of correlated quantum sources, and a proposal for a program to obtain operational meaning for quantum conditional entropy. An appendix features the introduction of a notation and calculus of entropy in quantum systems.