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arXiv:quant-ph/0211170 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Entanglement-assisted capacity of constrained channels

A. S. Holevo

Published Jul 23, 2003• 24 citations
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Abstract

In this paper we fil a gap in previous work by proving the conjectured formula for the antanglement-assisted capacity of quantum channel with additive input constraint (such as Bosonic Gaussian channel). The main tools are the coding theorem for classical-quantum constrained channels and a finite dimensional approximation of the input density operators for the entanglement-assisted capacity.

DOI
10.1117/12.517873

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In this paper we fil a gap in previous work by proving the conjectured formula for the antanglement-assisted capacity of quantum channel with additive input constraint (such as Bosonic Gaussian channel). The main tools are the coding theorem for classical-quantum constrained channels and a finite dimensional approximation of the input density operators for the entanglement-assisted capacity.
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; embedding of the classical input in quantum input is always possible, and therefore the classical entanglement-assisted capacity C ea under an appropriate input constraint is well defined. We prove the general property of entropy increase for a weak complementary channel, which implies the equality C = C ea (where C is the unassisted capacity) for a certain class of c-q Gaussian channels under an appropriate energy-type constraint. On the other hand, we show by an explicit example that the inequality C < C ea is not unusual for constrained c-q Gaussian channel.
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity Ceaunder appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C = Cea(where C is the unassisted capacity) for certain class of c-q Gaussian channels under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality Ceais not unusual for constrained c-q Gaussian channel.
The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and the χχχ-capacity of constrained channels are obtained and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between the coherent information and the measure of privacy of classical information transmission by infinite-dimensional quantum channel is proved.
A coding theorem for entanglement-assisted communication via an infinite-dimensional quantum channel with linear constraints is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and χ-capacity of constrained channels are obtained, and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between coherent information and the measure of privacy of classical information transmission via an infinite-dimensional quantum channel is proved.
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality C