Geodesic
On Channels with Finite Holevo Capacity
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 732-750 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the nontrivial class of infinite dimensional quantum channels, characterized by the finiteness of the Holevo capacity. The sufficient conditions of existence of an optimal measure are obtained and examples of channels with no optimal measure are constructed.
Keywords: quantum state, quantum channel, quantum entropy, Holevo capacity. 
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M. E. Shirokov. On Channels with Finite Holevo Capacity. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 4, pp. 732-750. http://geodesic.mathdoc.fr/item/TVP_2008_53_4_a4/

[1] Bratteli U., Robinson D., Operatornye algebry i kvantovaya statisticheskaya mekhanika, Mir, M., 1982, 511 pp. | MR | Zbl

[2] Verner R. F., Kholevo A. S., Shirokov M. E., “O ponyatii stseplennosti v gilbertovykh prostranstvakh”, Uspekhi matem. nauk, 60:2 (2005), 153–154 | MR

[3] Kholevo A. S., Vvedenie v kvantovuyu teoriyu informatsii, MTsNMO, M., 2002, 126 pp.

[4] Kholevo A. S., Statisticheskaya struktura kvantovoi teorii, IKI, M., Izhevsk, 2003, 191 pp.

[5] Kholevo A. S., “Klassicheskaya propusknaya sposobnost kvantovykh kanalov s ogranicheniyami”, Teoriya veroyatn. i ee primen., 48:2 (2003), 359–374 | MR | Zbl

[6] Kholevo A. S., Shirokov M. E., “Nepreryvnye ansambli i klassicheskaya propusknaya sposobnost kvantovykh kanalov beskonechnoi razmernosti”, Teoriya veroyatn. i ee primen., 50:1 (2005), 98–114 | MR

[7] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989, 623 pp. | MR

[8] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974, 479 pp. | MR | Zbl

[9] Shirokov M. E., “O svoistvakh kvantovykh kanalov, svyazannykh s klassicheskoi propusknoi sposobnostyu”, Teoriya veroyatn. i ee primen., 52:2 (2007), 301–335

[10] Shirokov M. E., “Entropiinye kharakteristiki podmnozhestv sostoyanii. I”, Izv. RAN, 70:6 (2006), 193–222 | MR | Zbl

[11] Shirokov M. E., “Entropiinye kharakteristiki podmnozhestv sostoyanii. II”, Izv. RAN, 71:1 (2007), 187–224 | MR | Zbl

[12] Alfsen E. M., Compact Convex Sets and Boundary Integrals, Springer-Verlag, New York, Heidelberg, 1971, 210 pp. | MR | Zbl

[13] Dell'Antonio G. F., “On the limits of sequences of normal states”, Comm. Pure Appl. Math., 20 (1967), 413–429 | MR

[14] Lindblad G., “Expectations and entropy inequalities for finite quantum systems”, Comm. Math. Phys., 39:2 (1974), 111–119 | DOI | MR | Zbl

[15] Lindblad G., “Completely positive maps and entropy inequalities”, Comm. Math. Phys., 40:2 (1975), 147–151 | DOI | MR | Zbl

[16] Horodecki M., Shor P. W., Ruskai M. B., “Entanglement breaking channels”, Rev. Math. Phys., 15:6 (2003), 629–641 ; arXiv: quant-ph/0302031 | DOI | MR | Zbl

[17] Shirokov M. E., “The Holevo capacity of infinite dimensional channels and the additivity problem”, Comm. Math. Phys., 262:1 (2006), 137–159 ; arXiv: quant-ph/0408009 | DOI | MR | Zbl

[18] Schumacher B., Westmoreland M., “Optimal signal ensembles”, Phys. Rev. A, 63 (2001), 022308 ; arXiv: quant-ph/9912122 | DOI

[19] Parthasarathy K., Probability Measures on Metric Spaces, Academic Press, New York, London, 1967, 276 pp. | MR | Zbl

[20] Wehrl A., “General properties of entropy”, Rev. Modern Phys., 50:2 (1978), 221–260 | DOI | MR