dorsal/arxiv
View SchemaOn entropic quantities related to the classical capacity of infinite dimensional quantum channels
| Authors | M. E. Shirokov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411091 |
| URL | https://arxiv.org/abs/quant-ph/0411091 |
| DOI | 10.1117/12.620512 |
| Journal | Theory of Probability and its Applications, Vol. 52, No. 2, (2007), 250-276 |
Abstract
In this paper we consider the $\chi$-function (the Holevo capacity of constrained channel) and the convex closure of the output entropy for arbitrary infinite dimensional channel. It is shown that the $\chi$-function of an arbitrary channel is a concave lower semicontinuous function on the whole state space, having continuous restriction to any set of continuity of the output entropy. The explicit representation for the convex closure of the output entropy is obtained and its properties are explored. It is shown that the convex closure of the output entropy coincides with the convex hull of the output entropy on the convex set of states with finite output entropy. Similarly to the case of the $\chi$-function, it is proved that the convex closure of the output entropy has continuous restriction to any set of continuity of output entropy. Some applications of these results to the theory of entanglement are discussed. The obtained properties of the convex closure of the output entropy make it possible to generalize to the infinite dimensional case the convex duality approach to the additivity problem.
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"abstract": "In this paper we consider the $\\chi$-function (the Holevo capacity of\nconstrained channel) and the convex closure of the output entropy for arbitrary\ninfinite dimensional channel.\n It is shown that the $\\chi$-function of an arbitrary channel is a concave\nlower semicontinuous function on the whole state space, having continuous\nrestriction to any set of continuity of the output entropy.\n The explicit representation for the convex closure of the output entropy is\nobtained and its properties are explored. It is shown that the convex closure\nof the output entropy coincides with the convex hull of the output entropy on\nthe convex set of states with finite output entropy. Similarly to the case of\nthe $\\chi$-function, it is proved that the convex closure of the output entropy\nhas continuous restriction to any set of continuity of output entropy. Some\napplications of these results to the theory of entanglement are discussed.\n The obtained properties of the convex closure of the output entropy make it\npossible to generalize to the infinite dimensional case the convex duality\napproach to the additivity problem.",
"arxiv_id": "quant-ph/0411091",
"authors": [
"M. E. Shirokov"
],
"categories": [
"quant-ph"
],
"doi": "10.1117/12.620512",
"journal_ref": "Theory of Probability and its Applications, Vol. 52, No. 2,\n (2007), 250-276",
"title": "On entropic quantities related to the classical capacity of infinite dimensional quantum channels",
"url": "https://arxiv.org/abs/quant-ph/0411091"
},
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