Entropy characteristics of subsets of states. I

Izvestiya Mathematics

Volumn 70, Issue 6, 2006, Pages 1265-1292

  Shirokov, M E ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947670915     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2006v070n06ABEH002346     Document Type: Article

References (20)

1. O. Bratteli and D. W. Robinson, Operator algebras and quantum statistical mechanics. Vol. 1. C*- and W*-algebras, algebras, symmetry groups, decomposition of states, Springer, New York-Heidelberg Berlin 1979; Russian transl., Mir, Moscow 1982.
2. D. F. Dell'Antonio, "On the limits of sequences of normal states", Comm. Pure Appl. Math. 20 (1967), 413-429.
3. M. J. Donald, "Further results on the relative entropy", Math. Proc. Cambridge Philos. Soc. 101 (1987), 363-373.
4. P. Harremoës and F. Topsøe, "Maximum entropy fundamentals", Entropy 3:3 (2001), 191-226.
5. P. Harremoës, "Information topologies with applications", Entropy, search, complexity (I. Csiszár, G. O. H. Katona, and G. Tardos, eds.), Bolyai Soc. Math. Stud., vol. 16, Springer, New York 2007, pp. 113-150.
6. A. D. Ioffe and V. M. Tikhomirov, Theory of extremal problems, Nauka, Moscow 1974; English transl., North-Holland, Amsterdam-New York-Oxford 1979.
7. L. D. Kudryavtsev, A course of mathematical analysis, Vysshaya Shkola, Moscow 1988. (Russian)
8. G. Lindblad, "Expectations and entropy inequalities for finite quantum systems", Comm. Math. Phys. 39:2 (1974), 111-119.
9. G. Lindblad, "Completely positive maps and entropy inequalities", Comm. Math. Phys. 40:2 (1975), 147-151.
10. M. Ohya and D. Petz, Quantum entropy and its use, Texts Monogr. Phys., Springer-Verlag, Berlin 1993.
11. K. R. Parthasarathy, Probability measures on metric spaces, Probab. Math. Statist., vol. 3, Academic Press, New York-London 1967.
12. T. A. Sarymsakov, Introduction to quantum probability theory, Fan, Tashkent 1985. (Russian)
13. B. Schumacher and M. D. Westmoreland, "Sending classical information via noisy quantum channels", Phys. Rev. A 56:1 (1997), 131-138.
14. B. Schumacher and M. Westmoreland, Optimal signal ensembles, arXiv: quant-ph/9912122.
15. M. E. Shirokov, "The Holevo capacity of infinite dimensional channels and the additivity problem", Comm. Math. Phys. 262:1 (2006), 137-159.
16. M. E. Shirokov, On entropic quantities related to the classical capacity of infinite dimensional quantum channels, arXiv: quant-ph/0411091.
17. A. S. Holevo, "Quantum coding theorems", Uspekhi Mat. Nauk 53:6 (1998), 193-230; English transl., Russian Math. Surveys 53 (1998), 1295-1331.
18. A. S. Holevo, "Entanglement-assisted capacities of constrained quantum channels", Teor. Veroyatn. Primen. 48 (2004), 359-374; English transl., Theory Probab. Appl. 48 (2004), 243-255.
19. A. S. Holevo and M. E. Shirokov, "Continuous ensembles and the capacity of infinite-dimensional channels", Teor. Veroyatn. Primen. 50 (2006), 98-114; English transl., Theory Probab. Appl. 50 (2006), 86-98.
20. A. Wehrl, "General properties of entropy", Rev. Mod. Phys. 50:2 (1978), 221-260.