On the chernoff bound for efficiency of quantum hypothesis testing

Annals of Statistics

Volumn 33, Issue 2, 2005, Pages 959-976

  Kargin, Vladislav ^a  

^a International Arbitration and Litigation Practice   (United States)

Author keywords

Entanglement; Fidelity; Joint measurement; Quantum relative entropy; Quantum statistics; Separate measurement

Indexed keywords

EID: 22944467816     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053604000001219     Document Type: Review

References (24)

1. BALLESTER, M. A. (2004). Estimation of unitary quantum operations. Phys. Rev. A 69 022303.
2. BARNDORFF-NIELSEN, O. E., GILL, R. D. and JUPP, P. E. (2003). On quantum statistical inference (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 65 775-816.
3. BENNETT, C. H., DIVINCENZO, D. P., FUCHS, C. A., MOR, T., RAINS, E., SHOR, P. W., SMOLIN, J. A. and WOOTTERS, W. K. (1999). Quantum nonlocality without entanglement. Phys. Rev. A 59 1070-1091.
4. CHERNOFF, H. (1952). A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Statist. 23 493-507.
5. CIRAC, J. I. and ZOLLER, P. (1995). Quantum computations with cold trapped ions. Phys. Rev. Lett. 74 4091-4094.
6. COVER, T. M. and THOMAS, J. A. (1991). Elements of Information Theory. Wiley, New York.
7. FUCHS, C. A. and CAVES, C. M. (1995). Mathematical techniques for quantum communication theory. Open Systems and Information Dynamics 3 345-356. Available at http://arxiv.org/abs/quant-ph/9604001.
8. FUCHS, C. A. and VAN DE GRAAF, J. (1999). Cryptographic distinguishability measures for quantum-mechanical states. IEEE Trans. Inform. Theory 45 1216-1227.
9. GILL, R. D. (2001). Asymptotics in quantum statistics. In State of the Art in Probability and Statistics 255-285. IMS, Beachwood, OH.
10. GILL, R. D. and MASSAR, S. (2000). State estimation for large ensembles. Phys. Rev. A 61 042312.
11. HELSTROM, C. W. (1976). Quantum Detection and Estimation Theory. Academic Press, New York.
12. HOEFFDING, W. (1965). Asymptotically optimal tests for multinomial distributions. Ann. Math. Statist. 36 369-401.
13. HOLEVO, A. S. (1976). Investigation of a general theory of statistical decisions. Trudy Mat. Inst. Steklov. 124.
14. [English translation in Proc. Steklov Inst. Math. 3 (1978) Amer. Math. Soc., Providence, RI.]
15. HOLEVO, A. S. (2001). Statistical Structure of Quantum Theory. Springer, Berlin.
16. KEYL, M. and WERNER, R. F. (2001). Estimating the spectrum of a density operator. Phys. Rev. A 64 052311.
17. NIELSEN, M. A. and CHUANG, I. L. (2000). Quantum Computation and Quantum Information. Cambridge Univ. Press.
18. OGAWA, T. and HAYASHI, M. (2002). On error exponents in quantum hypothesis testing. Available at http://arxiv.org/abs/quant-ph/0206151.
19. OGAWA, T. and NAGAOKA, H. (2000). Strong converse and Stein's lemma in quantum hypothesis testing. IEEE Trans. Inform. Theory 46 2428-2433.
20. PARTHASARATHY, K. R. (2001). On consistency of the maximum likelihood method in testing multiple quantum hypotheses. In Stochastics in Finite and Infinite Dimensions (T. Hida et al., eds.) 361-377. Birkhäuser, Boston.
21. PERES, A. (1995). Quantum Theory: Concepts and Methods. Kluwer, Dordrecht.
22. SANOV, I. N. (1957). On the probability of large deviations of random variables. Mat. Sb. N. S. 42 11-44.
23. SANTALÓ, L. A. (1976). Integral Geometry and Geometric Probability. Addison-Wesley, Reading, MA.
24. TURCHETTE, Q. A., WOOD, C. S., KING, B. E., MYATT, C. J., LEIBFRIED, D., ITANO, W. M., MONROE, C. and WINELAND, D. J. (1998). Deterministic entanglement of two trapped ions. Phys. Rev. Lett. 81 3631-3634.