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Theory of Probability and Its Applications

Coding Theorems for Hybrid Channels

A. A. Kuznetsova, A. S. Holevo

Published Jan 1, 2014• 4 citations
Publisher

Abstract

The main result of this paper is the coding theorem for the entanglement-assisted capacity of measurement channel with arbitrary alphabet (Theorem \refcea). As a by-product, a number of results concerning entropies of hybrid (classical-quantum) systems are obtained, as well as the capacities of channels with hybrid output, which are used in the proof of Theorem 3.

DOI
10.1137/s0040585x97986527

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The main result of this paper is the coding theorem for the entanglement-assisted capacity of measurement channel with arbitrary alphabet (Theorem \refcea). As a by-product, a number of results concerning entropies of hybrid (classical-quantum) systems are obtained, as well as the capacities of channels with hybrid output, which are used in the proof of Theorem 3.
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.
Contents I. Introduction II. General considerations § 1. Quantum communication channel § 2. Entropy bound and channel capacity § 3. Formulation of the quantum coding theorem. Weak conversion III. Proof of the direct statement of the coding theorem § 1. Channels with pure signal states § 2. Reliability function § 3. Quantum binary channel § 4. Case of arbitrary states with bounded entropy IV. c-q channels with input constraints § 1. Coding theorem § 2. Gauss channel with one degree of freedom § 3. Classical signal on quantum background noise Bibliography