dorsal/arxiv
View SchemaThe Convex Closure of the Output Entropy of Infinite Dimensional Channels and the Additivity Problem
| Authors | M. E. Shirokov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608090 |
| URL | https://arxiv.org/abs/quant-ph/0608090 |
| Journal | Russian Mathematical Surveys, Vol. 61, No. 6, (2006), 1186--1188 |
Abstract
The 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.
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"abstract": "The continuity properties of the convex closure of the output entropy of\ninfinite dimensional channels and their applications to the additivity problem\nare considered.\n The main result of this paper is the statement that the superadditivity of\nthe convex closure of the output entropy for all finite dimensional channels\nimplies the superadditivity of the convex closure of the output entropy for all\ninfinite dimensional channels, which provides the analogous statements for the\nstrong superadditivity of the EoF and for the additivity of the minimal output\nentropy.\n The above result also provides infinite dimensional generalization of Shor\u0027s\ntheorem stated equivalence of different additivity properties.\n The superadditivity of the convex closure of the output entropy (and hence\nthe additivity of the minimal output entropy) for two infinite dimensional\nchannels with one of them a direct sum of noiseless and entanglement-breaking\nchannels are derived from the corresponding finite dimensional results.\n In the context of the additivity problem some observations concerning\ncomplementary infinite dimensional channels are considered.",
"arxiv_id": "quant-ph/0608090",
"authors": [
"M. E. Shirokov"
],
"categories": [
"quant-ph",
"math-ph",
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],
"journal_ref": "Russian Mathematical Surveys, Vol. 61, No. 6, (2006), 1186--1188",
"title": "The Convex Closure of the Output Entropy of Infinite Dimensional Channels and the Additivity Problem",
"url": "https://arxiv.org/abs/quant-ph/0608090"
},
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