dorsal/arxiv
View SchemaOn Shor's channel extension and constrained channels
| Authors | A. S. Holevo, M. E. Shirokov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0306196 |
| URL | https://arxiv.org/abs/quant-ph/0306196 |
| DOI | 10.1007/s00220-004-1116-5 |
| Journal | Commun. Math. Phys. v. 249,417-430, 2004 |
Abstract
In this paper we give several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity. To this end a characteristic property of the optimal ensemble for such a channel is derived, generalizing the maximal distance property. It is shown that the additivity conjecture for constrained channels holds true for certain nontrivial classes of channels. Recently P. Shor showed that conjectured additivity properties for several quantum information quantities are in fact equivalent. After giving an algebraic formulation for the Shor's channel extension, its main asymptotic property is proved. It is then used to show that additivity for two constrained channels can be reduced to the same problem for unconstrained channels, and hence, "global" additivity for channels with arbitrary constraints is equivalent to additivity without constraints.
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"abstract": "In this paper we give several equivalent formulations of the additivity\nconjecture for constrained channels, which formally is substantially stronger\nthan the unconstrained additivity. To this end a characteristic property of the\noptimal ensemble for such a channel is derived, generalizing the maximal\ndistance property. It is shown that the additivity conjecture for constrained\nchannels holds true for certain nontrivial classes of channels.\n Recently P. Shor showed that conjectured additivity properties for several\nquantum information quantities are in fact equivalent. After giving an\nalgebraic formulation for the Shor\u0027s channel extension, its main asymptotic\nproperty is proved. It is then used to show that additivity for two constrained\nchannels can be reduced to the same problem for unconstrained channels, and\nhence, \"global\" additivity for channels with arbitrary constraints is\nequivalent to additivity without constraints.",
"arxiv_id": "quant-ph/0306196",
"authors": [
"A. S. Holevo",
"M. E. Shirokov"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s00220-004-1116-5",
"journal_ref": "Commun. Math. Phys. v. 249,417-430, 2004",
"title": "On Shor\u0027s channel extension and constrained channels",
"url": "https://arxiv.org/abs/quant-ph/0306196"
},
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