Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel

Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a... Several relations between the Holevo capacity and entanglement-assisted classical capacity of a quantum channel are proved; necessary and sufficient conditions for their coincidence are obtained. In particular, it is shown that these capacities coincide if (respectively, only if) the channel (respectively, the χ-essential part of the channel) belongs to the class of classical-quantum channels (the χ-essential part is a restriction of a channel obtained by discarding all states that are useless for transmission of classical information). The obtained conditions and their corollaries are generalized to channels with linear constraints. By using these conditions it is shown that the question of coincidence of the Holevo capacity and entanglement-assisted classical capacity depends on the form of a constraint. Properties of the difference between quantum mutual information and the χ-function of a quantum channel are explored. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Engineering; Information Storage and Retrieval; Systems Theory, Control; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946012020019
Publisher site
See Article on Publisher Site

Abstract

Several relations between the Holevo capacity and entanglement-assisted classical capacity of a quantum channel are proved; necessary and sufficient conditions for their coincidence are obtained. In particular, it is shown that these capacities coincide if (respectively, only if) the channel (respectively, the χ-essential part of the channel) belongs to the class of classical-quantum channels (the χ-essential part is a restriction of a channel obtained by discarding all states that are useless for transmission of classical information). The obtained conditions and their corollaries are generalized to channels with linear constraints. By using these conditions it is shown that the question of coincidence of the Holevo capacity and entanglement-assisted classical capacity depends on the form of a constraint. Properties of the difference between quantum mutual information and the χ-function of a quantum channel are explored.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jul 13, 2012

References

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