"Extrinsic" and "Intrinsic" Data in Quantum Measurements: Asymptotic Convex Decomposition of Positive Operator Valued Measures

Communications in Mathematical Physics

Volumn 244, Issue 1, 2004, Pages 157-185

  Winter, Andreas ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0742323589     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0989-z     Document Type: Article

References (32)

1. Ahlswede, R., Löber, P.: Quantum Data Processing. IEEE Trans. Inf. Theory 47(1), 474-478 (2001)
2. Ahlswede, R., Winter, A.: Strong converse for identification via quantum channels. IEEE Trans. Inf. Theory 48(3), 569-579 (2002)
3. Bennett, C.H., Shor, P.W., Smolin, J.A., Thapliyal, A.V.: Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem. IEEE Trans. Inf. Theory 48(10), 2637-2655 (2002)
4. Bennett, C.H., Devetak, I., Harrow, A., Shor, P.W., Winter, A.: The Quantum Reverse Shannon Theorem. In preparation
5. Bhatia, R.: Matrix Analysis. Graduate Texts in Mathematics 169, Berlin-New York: Springer Verlag, 1997
6. Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra Appl. 10, 285-290 (1975)
7. Davies, E.B., Lewis, J.T.: An operational approach to quantum probability. Commun. Math. Phys. 17, 239-260 (1970)
8. Fano, R.M.: Class Notes for Transmission of Information. Course 6.574, MIT, Cambridge MA, 1952. See also R. M. Fano, Transmission of Information, New York: Wiley and Sons, 1961
9. Fano, R.M.: Class Notes for Transmission of Information. Course 6.574, MIT, Cambridge MA, 1952. See also R. M. Fano, Transmission of Information, New York: Wiley and Sons, 1961
10. Fuchs, C.A., van de Graaf, J.: Cryptographic Distinguishability Measures for Quantum-Mechanical States. IEEE Trans. Inf. Theory 45(4), 1216-1227 (1999)
11. Hausladen, P., Wootters, W.K.: A 'pretty good' measurement for distinguishing quantum states. J. Modern Opt. 41(12), 2385-2390 (1994)
12. Helstrom, C.W.: Quantum Detection and Estimation Theory. New York: Academic Press, 1976
13. Holevo, A.S.: Information-theoretical aspects of quantum measurement. Probl. Inf. Transm. 9(2), 110-118 (1973)
14. Holevo, A.S.: Bounds for the quantity of information transmitted by a quantum channel. Probl. Inf. Transm. 9(3), 177-183 (1973)
15. Holevo, A.S.: Asymptotically optimal hypotheses testing in quantum statistics. Theor. Probability Appl. 23(2), 411-415 (1979)
16. Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. Amsterdam: North Holland, 1982
17. Holevo, A.S.: The Capacity of the Quantum Channel with General Signal States. IEEE Trans. Inf. Theory 44(1), 269-273 (1998)
18. Hughston, L.P., Jozsa, R., Wootters, W.K.: A complete classification of quantum ensembles having a given density matrix. Phys. Lett. A 183(1), 14-18 (1993)
19. Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Optics 41, 2315-2323 (1994)
20. Lehmann, E.L., Casella, G.: Theory of Point Estimation. 2nd edition, Springer Texts in Statistics, Berlin-New York: Springer, 1998
21. Lebedev, D.S., Levitin, L.B.: The maximum amount of information transmissible by an electromagnetic field. Dokl. Akad. Nauk (SSSR) 149(6), 1299-1302 (1963) (Russian). [English translation: Soviet Physics Dokl. 8, 377-379 (1963)]
22. Lebedev, D.S., Levitin, L.B.: The maximum amount of information transmissible by an electromagnetic field. Dokl. Akad. Nauk (SSSR) 149(6), 1299-1302 (1963) (Russian). [English translation: Soviet Physics Dokl. 8, 377-379 (1963)]
23. Lindblad, G.: Quantum entropy and quantum measurements. In: C. Bendjaballah, O. Hirota, S. Reynaud, (eds.), Quantum Aspects of Optical Communications, Lecture Notes in Physics, Vol. 378, Berlin: Springer Verlag, 1991, pp. 71-80
24. Massar, S., Popescu, S.: Amount of information obtained by a quantum measurement. Phys. Rev. A 61, 062303 (2000)
25. Schumacher, B.: Sending entanglement through noisy quantum channels. Phys. Rev. A 54(4), 2614-2628 (1996)
26. Schumacher, B., Westmoreland, M.D.: Sending classical information via noisy quantum channels. Phys. Rev. A 56(1), 131-138 (1997)
27. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423 and 623-656 (1948)
28. Stinespring, W.K: Positive functions on C*-algebras. Proc. Am. Math. Soc. 6, 211-216 (1955)
29. Uhlmann, A.: The 'transition probability' in the state space of a *-algebra. Rep. Math. Phys. 9, 273-279 (1976)
30. Winter, A.: Coding Theorem and Strong Converse for Quantum Channels. IEEE Trans. Inf. Theory 45(7), 2481-2485 (1999)
31. Winter, A., Massar, S.: Compression of quantum-measurement operations. Phys. Rev. A. 64 012311 (2001)
32. Wolfowitz, J.: Coding Theorems of Information Theory. 2nd edition, Berlin: Springer Verlag, 1964