The Convex Closure of the Output Entropy of Infinite Dimensional Channels and the Additivity Problem

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dc.creatorShirokov, M. E.
dc.date2006-08-10
dc.date.accessioned2026-07-07T12:13:25Z
dc.date.available2026-07-07T12:13:25Z
dc.descriptionThe continuity properties of the convex closure of the output entropy of infinite dimensional channels and their applications to the additivity problem are considered. The main result of this paper is the statement that the superadditivity of the convex closure of the output entropy for all finite dimensional channels implies the superadditivity of the convex closure of the output entropy for all infinite dimensional channels, which provides the analogous statements for the strong superadditivity of the EoF and for the additivity of the minimal output entropy. The above result also provides infinite dimensional generalization of Shor's theorem stated equivalence of different additivity properties. The superadditivity of the convex closure of the output entropy (and hence the additivity of the minimal output entropy) for two infinite dimensional channels with one of them a direct sum of noiseless and entanglement-breaking channels are derived from the corresponding finite dimensional results. In the context of the additivity problem some observations concerning complementary infinite dimensional channels are considered.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/quant-ph/0608090
dc.identifierhttp://arxiv.org/abs/quant-ph/0608090
dc.identifierRussian Mathematical Surveys, Vol. 61, No. 6, (2006), 1186--1188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210840
dc.subjectQuantum Physics
dc.subjectMathematical Physics
dc.titleThe Convex Closure of the Output Entropy of Infinite Dimensional Channels and the Additivity Problem
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