Geodesic
Entropy characteristics of subsets of states. II
Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 181-218.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study properties of the $\chi$-capacity (regarded as a function of sets of quantum states) in the infinite-dimensional case. We consider various subsets of states and determine their $\chi$-capacity and optimal average. We construct counterexamples that illustrate general results. The possibility of “finite-dimensional approximations” of the $\chi$-capacity and optimal average is shown for an arbitrary set of quantum states. 
@article{IM2_2007_71_1_a8,
     author = {M. E. Shirokov},
     title = {Entropy characteristics of subsets of states. {II}},
     journal = {Izvestiya. Mathematics },
     pages = {181--218},
     publisher = {mathdoc},
     volume = {71},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a8/}
}
TY  - JOUR
AU  - M. E. Shirokov
TI  - Entropy characteristics of subsets of states. II
JO  - Izvestiya. Mathematics 
PY  - 2007
SP  - 181
EP  - 218
VL  - 71
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a8/
LA  - en
ID  - IM2_2007_71_1_a8
ER  - 
%0 Journal Article
%A M. E. Shirokov
%T Entropy characteristics of subsets of states. II
%J Izvestiya. Mathematics 
%D 2007
%P 181-218
%V 71
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a8/
%G en
%F IM2_2007_71_1_a8
M. E. Shirokov. Entropy characteristics of subsets of states. II. Izvestiya. Mathematics , Tome 71 (2007) no. 1, pp. 181-218. http://geodesic.mathdoc.fr/item/IM2_2007_71_1_a8/

[1] R. F. Verner, A. S. Kholevo, M. E. Shirokov, “O ponyatii stseplennosti v gilbertovom prostranstve”, UMN, 60:2 (2005), 153–154 | MR | Zbl

[2] A. D. Ioffe, V. M. Tikhomirov, Teoriya ekstremalnykh zadach, Nauka, M., 1974 ; A. D. Ioffe, V. M. Tihomirov, Theory of extremal problems, Stud. Math. Appl., 6, North-Holland, Amsterdam, 1979 | MR | Zbl | MR | Zbl

[3] L. D. Kudryavtsev, Kurs matematicheskogo analiza, Vysshaya shkola, M., 1988 | MR | Zbl

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

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

[6] M. Ohya, D. Petz, Quantum entropy and its use, Texts and Monographs in Physics, Springer-Verlag, Berlin, 1993 | MR | Zbl

[7] K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, 3, Academic Press, New York–London, 1967 | MR | Zbl

[8] K. R. Parthasarathy, Extremal quantum states in coupled systems, arXiv.org: quant-ph/0307182 | MR

[9] A. S. Kholevo, “Kvantovye teoremy kodirovaniya”, UMN, 53:6 (1998), 193–230 | MR | Zbl

[10] A. S. Kholevo, Statisticheskaya struktura kvantovoi teorii, IKI, M., Izhevsk, 2003; A. S. Holevo, Statistical structure of quantum theory, Lecture Notes in Physics. New Series m: Monographs, Springer, Berlin, 2001 | MR | Zbl

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

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

[13] P. W. Shor, “Capacities of quantum channels and how to find them”, Math. Program., 97:1–2 (2003), 311–335 ; arXiv.org: quant-ph/0304102 | DOI | MR | Zbl

[14] A. Wehrl, “General properties of entropy”, Rev. Mod. Phys., 50 (1978), 221–250 | DOI | MR