Entropy reduction of quantum measurements

Journal of Mathematical Physics

Volumn 52, Issue 5, 2011, Pages

  Shirokov, M E ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79957891777     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3589831     Document Type: Article

References (25)

1. Adami C. Cerf N.J. Von Neumann capacity of noisy quantum channels. Phys. Rev. A. 1997, 56:3470. 10.1103/PhysRevA.56.3470, and ;e-print arXiv:quant-ph/9609024.
2. Barchielli A. Lupieri G. Instruments and mutual entropies in quantum information. Banach Center Publications 2006, 73:65. 10.4064/bc73, and ;e-print arXiv:quant-ph/0412116.
3. Bratteli O. Robinson D.W. Operators algebras and quantum statistical mechanics 1979, I. and (Springer Verlag, New York-Heidelberg-Berlin)Vol.
4. Buscemi F. Hayashi M. Horodecki M. Global information balance in quantum measurements. Phys. Rev. Lett. 2008, 100:210504. 10.1103/PhysRevLett.100.210504.
5. Davies E.B. Lewis J.T. An operational approach to quantum probability. Commun. Math. Phys 1970, 17:239. 10.1007/BF01647093.
6. Groenewold H.J. A problem of information gain by quantum measurements. Int. J. Theor. Phys. 1971, 4:327. 10.1007/BF00815357.
7. Holevo A.S. On complementary channels and the additivity problem. Probab. Theory Appl. 2007, 51:92. 10.1137/S0040585X97982244, e-print arXiv:quant-ph/0509101.
8. Holevo A.S. Shirokov M.E. Mutual and Coherent Information for Infinite-Dimensional Quantum Channels. Probl. Inf. Transm. 2010, 46:201. 10.1134/S0032946010030014, and ;e-print arXiv:1004.2495 [math-ph].
9. Holevo A.S. Statistical structure of quantum theory 2001, (Springer-Verlag, Berlin, ).
10. Holevo A.S. Radon-Nikodym derivatives of quantum instruments. J. Math. Phys. 1998, 39:1373. 10.1063/1.532385.
11. Jacobs K. A bound on the mutual information, and properties of entropy reduction for quantum channels with inefficient measurements. J. Math. Phys. 2006, 47:012102. 10.1063/1.2158433.
12. Lindblad G. An entropy inequality for quantum measurement. Commun. Math. Phys. 1972, 28:245. 10.1007/BF01645778.
13. Lindblad G. Expectation and Entropy Inequalities for Finite Quantum Systems. Commun. Math. Phys. 1974, 39:111. 10.1007/BF01608390.
14. Loubenets E.R. Quantum stochastic approach to the description of quantum measurements. J. Phys. A 2001, 34:7639. 10.1088/0305-4470/34/37/316.
15. Luo S. Information conservation and entropy change in quantum measurements. Phys. Rev. A 2010, 82:052103. 10.1103/PhysRevA.82.052103.
16. King C. Matsumoto K. Nathanson M. Ruskai M.B. Properties of Conjugate Channels with Applications to Additivity and Multiplicativity. Markov Processes Relat. Fields 2007, 13:391. and and.
17. Nielsen M.A. Chuang I.L. Quantum Computation and Quantum Information 2000, and (Cambridge University Press, Cambridge, England, ).
18. Ohya M. Petz D. Quantum Entropy and Its Use. Texts and Monographs in Physics 1993, (Springer-Verlag, Berlin, ).
19. Ozawa M. Quantum measuring processes of continuous observables. J. Math. Phys. 1984, 25:79. 10.1063/1.526000.
20. Ozawa M. Conditional Probability and A Posteriori States in Quantum Mechanics. Publ. RIMS, Kyoto Univ. 1985, 21:279. 10.2977/prims/1195179625.
21. Ozawa M. On information gain by quantum measurement of continuous observable. J. Math. Phys. 1986, 27:759. 10.1063/1.527179.
22. Parthasarathy K. Probability measures on metric spaces 1967, (Academic, New York and London, ).
23. Shirokov M.E. Continuity of the von Neumann entropy. Commun. Math. Phys. 2010, 296:625. 10.1007/s00220-010-1007-x, e-print arXiv:0904.1963 [math-ph].
24. In Ref. 21, the term quasicomplete is used. The term irreducible seems to be more reasonable, it appeared in Ref. 19 and is used in the subsequent papers.
25. A quantum operation Φ is called entanglement-breaking if for an arbitrary state ω in where is a separable Hilbert space, the operator belongs to the convex closure of the product-operators A⊗B.