NDLI: Continuous Ensembles and the Capacity of Infinite-Dimensional Quantum Channels

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Holevo, A. S. Shirokov, M. E.
Copyright Year	2006
Abstract	This paper is devoted to the study of $\chi$-capacity, closely related to the classical capacity of infinite-dimensional quantum channels. For such channels generalized ensembles are defined as probability measures on the set of all quantum states. We establish the compactness of the set of generalized ensembles with averages in an arbitrary compact subset of states. This result enables us to obtain a sufficient condition for the existence of the optimal generalized ensemble for an infinite-dimensional channel with input constraint. This condition is shown to be fulfilled for Bosonic Gaussian channels with constrained mean energy. In the case of convex constraints, a characterization of the optimal generalized ensemble extending the "maximal distance property" is obtained.
Starting Page	86
Ending Page	98
Page Count	13
File Format	PDF
ISSN	0040585X
DOI	10.1137/S0040585X97981470
e-ISSN	10957219
Journal	Theory of Probability & Its Applications (TPRBAU)
Issue Number	1
Volume Number	50
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	generalized ensemble quantum channel $\chi$-capacity
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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Continuous Ensembles and the Capacity of Infinite-Dimensional Quantum Channels