On channels with finite Holevo capacity

Details On channels with finite Holevo capacity On channels with finite Holevo capacity

2006-02-07

arxiv.org/abs/quant-ph/0602073v1

Theory of Probability and its Applications, Vol. 53, No. 4, (2008), 732-750

Physics

Quantum Physics

23 pages

Scientific paper

We consider a nontrivial class of infinite dimensional quantum channels characterized by finiteness of the Holevo capacity. Some general properties of channels of this class are described. In particular, a special sufficient condition of existence of an optimal measure is obtained and examples of channels with no optimal measure are constructed. It is shown that each channel with finite Holevo capacity has a natural extension to the set of all positive normalized functionals on the algebra of all bounded operators. General properties of such an extension are described. The class of infinite dimensional channels, for which the Holevo capacity can be explicitly determined, is considered.

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