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Volumn 37, Issue 2, 2009, Pages 1040-1057

The Chernoff lower bound for symmetric quantum hypothesis testing

Author keywords

Bayesian discrimination; Density operators; Exponential error rate; Holevo Helstrom tests; Quantum Chernoff bound; Quantum statistics

Indexed keywords


EID: 63849189355     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOS593     Document Type: Article
Times cited : (251)

References (21)
  • 2
  • 4
    • 40849085551 scopus 로고    scopus 로고
    • The quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian states
    • CALSAMIGLIA, J., MASANES, L., MUNOZ- TAPIA, R., ACIN, A. and BAGAN, E. (2008). The quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian states. Phys. Rev. A 77 032311.
    • (2008) Phys. Rev. A , vol.77 , pp. 032311
    • CALSAMIGLIA, J.1    MASANES, L.2    MUNOZ- TAPIA, R.3    ACIN, A.4    BAGAN, E.5
  • 5
    • 0038178392 scopus 로고
    • Natural geometry of families of probability laws. Results in Science and Technology
    • MR1128374, In Russian
    • CHENTSOV, N. N. and MOROZOVA, E. A. (1991). Natural geometry of families of probability laws. Results in Science and Technology. Ser. Modern Problems of Mathematics. Fundamental Trends 83 133-265. (In Russian.) MR1128374
    • (1991) Ser. Modern Problems of Mathematics. Fundamental Trends , vol.83 , pp. 133-265
    • CHENTSOV, N.N.1    MOROZOVA, E.A.2
  • 6
    • 0000182415 scopus 로고
    • A measure of asymptotic efficiency of tests of a hypothesis based on the sum of observations
    • MR0057518
    • CHERNOFF, H. (1952). A measure of asymptotic efficiency of tests of a hypothesis based on the sum of observations. Ann. Math. Statist. 23 493-507. MR0057518
    • (1952) Ann. Math. Statist , vol.23 , pp. 493-507
    • CHERNOFF, H.1
  • 7
    • 84889281816 scopus 로고    scopus 로고
    • COVER, T.M. and THOMAS, J. A. (1991). Elements of Information Theory.Wiley, New York. MR1122806
    • COVER, T.M. and THOMAS, J. A. (1991). Elements of Information Theory.Wiley, New York. MR1122806
  • 8
    • 0032667067 scopus 로고    scopus 로고
    • Cryptographic distinguishability measures for quantum-mechanical states
    • MR1686254
    • FUCHS, C. A. and VAN DE GRAAF, J. (1999). Cryptographic distinguishability measures for quantum-mechanical states. IEEE Trans. Inform. Theory 45 1216-1227. MR1686254
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 1216-1227
    • FUCHS, C.A.1    VAN DE GRAAF, J.2
  • 9
    • 65349101851 scopus 로고    scopus 로고
    • GILL, R. (2001). Asymptotics in quantum statistics. In State of the Art in Probability and Statistics (A. W. van der Vaart, M. de Gunst and C. A. J. Klaassen, eds.). IMS Lecture Notes Monogr. Ser. 36 255-285. IMS, Beachwood, OH. Also available at arXiv:math/0405571v1. MR1836565
    • GILL, R. (2001). Asymptotics in quantum statistics. In State of the Art in Probability and Statistics (A. W. van der Vaart, M. de Gunst and C. A. J. Klaassen, eds.). IMS Lecture Notes Monogr. Ser. 36 255-285. IMS, Beachwood, OH. Also available at arXiv:math/0405571v1. MR1836565
  • 11
    • 0002499298 scopus 로고
    • The proper formula for relative entropy and its asymptotics in quantum probability
    • MR1139426
    • HIAI, F. and PETZ, D. (1991). The proper formula for relative entropy and its asymptotics in quantum probability. Comm. Math. Phys. 143 99-114. MR1139426
    • (1991) Comm. Math. Phys , vol.143 , pp. 99-114
    • HIAI, F.1    PETZ, D.2
  • 12
    • 0001613029 scopus 로고
    • Asymptotically optimal tests for multinomial distributions
    • MR0173322
    • HOEFFDING, W. (1965). Asymptotically optimal tests for multinomial distributions. Ann. Math. Statist. 36 369-408. MR0173322
    • (1965) Ann. Math. Statist , vol.36 , pp. 369-408
    • HOEFFDING, W.1
  • 13
    • 0347070782 scopus 로고
    • Investigations in the general theory of statistical decisions
    • In Russian
    • HOLEVO, A. S. (1978). Investigations in the general theory of statistical decisions. Trudy Mat. Inst. Steklov 124. (In Russian.)
    • (1978) Trudy Mat. Inst. Steklov , vol.124
    • HOLEVO, A.S.1
  • 14
    • 65349117781 scopus 로고    scopus 로고
    • [English translation in Proc. Steklov Inst. of Math. 3 (1978) Amer. Math. Soc., Providence, RI.] MR0652516
    • [English translation in Proc. Steklov Inst. of Math. 3 (1978) Amer. Math. Soc., Providence, RI.] MR0652516
  • 15
    • 22944467816 scopus 로고    scopus 로고
    • On the Chernoff bound for efficiency of quantum hypothesis testing
    • MR2163165
    • KARGIN, V. (2005). On the Chernoff bound for efficiency of quantum hypothesis testing. Ann. Statist. 33 959-976. MR2163165
    • (2005) Ann. Statist , vol.33 , pp. 959-976
    • KARGIN, V.1
  • 16
    • 65349097533 scopus 로고    scopus 로고
    • MOSONYI, M. (2008). Hypothesis testing for Gaussian states on bosonic lattices. Available at arXiv:0808.1450v1.
    • MOSONYI, M. (2008). Hypothesis testing for Gaussian states on bosonic lattices. Available at arXiv:0808.1450v1.
  • 17
    • 85174220945 scopus 로고    scopus 로고
    • NIELSEN, M. and CHUANG, I. (2000). Quantum Computation and Quantum Information. Cambridge Univ. Press. MR1796805
    • NIELSEN, M. and CHUANG, I. (2000). Quantum Computation and Quantum Information. Cambridge Univ. Press. MR1796805
  • 18
    • 33847645203 scopus 로고    scopus 로고
    • A lower bound of Chernoff type for symmetric quantum hypothesis testing. Available at arXiv
    • quant-ph/0607216
    • NUSSBAUM, M. and SZKOLA, A. (2006). A lower bound of Chernoff type for symmetric quantum hypothesis testing. Available at arXiv:quant-ph/0607216.
    • (2006)
    • NUSSBAUM, M.1    SZKOLA, A.2
  • 19
    • 2942640136 scopus 로고    scopus 로고
    • On error exponents in quantum hypothesis testing
    • MR2094898
    • OGAWA, T. andHAYASHI, M. (2004). On error exponents in quantum hypothesis testing. IEEE Trans. Inform. Theory 50 1368-1372. MR2094898
    • (2004) IEEE Trans. Inform. Theory , vol.50 , pp. 1368-1372
    • OGAWA, T.1    andHAYASHI, M.2
  • 20
    • 0009909847 scopus 로고
    • On the probability of large deviations of random variables
    • In Russian
    • SANOV, I. N. (1957). On the probability of large deviations of random variables. Mat. Sbornik 42 11-44. (In Russian.)
    • (1957) Mat. Sbornik , vol.42 , pp. 11-44
    • SANOV, I.N.1
  • 21
    • 65349105539 scopus 로고    scopus 로고
    • [English translation in Selected Translat. Math. Stat. 1 213-244 (1961).] MR0116378
    • [English translation in Selected Translat. Math. Stat. 1 213-244 (1961).] MR0116378


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.