On Asymptotically Optimal Hypothesis Testing in Quantum Statistics
Александр Семенович Холево · Theory of Probability and Its Applications · 1979
Previous article Next article On Asymptotically Optimal Hypothesis Testing in Quantum StatisticsA. S. KholevoA. S. Kholevohttps://doi.org/10.1137/1123048PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. S. Holevo, Statistical decision theory for quantum systems, J. Multivariate Anal., 3 (1973), 337–394 10.1016/0047-259X(73)90028-6 MR0337245 0275.62004 CrossrefGoogle Scholar[2] C. W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, N. Y., 1976 Google Scholar[3] Horace P. Yuen, , Robert S. Kennedy and , Melvin Lax, Optimum testing of multiple hypotheses in quantum detection theory, IEEE Trans. Information Theory, IT-21 (1975), 125–134 10.1109/TIT.1975.1055351 MR0397511 0301.94001 CrossrefGoogle Scholar[4] A. S. Kholevo, Remarks on optimal quantum measurements, Problems in Transmission of Information, 10 (1974), 51–55, (In Russian.) 0309.94001 Google Scholar[5] Robert Schatten, Norm ideals of completely continuous operators, Second printing. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 27, Springer-Verlag, Berlin, 1970vii+81 MR0257800 0188.44103 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Quantum Algorithm for Petz Recovery Channels and Pretty Good MeasurementsPhysical Review Letters, Vol. 128, No. 22 | 1 June 2022 Cross Ref Fast algorithm for quantum polar decomposition and applicationsPhysical Review Research, Vol. 4, No. 1 | 22 February 2022 Cross Ref Reversing Lindblad Dynamics via Continuous Petz Recovery MapPhysical Review Letters, Vol. 128, No. 2 | 11 January 2022 Cross Ref Symmetric distinguishability as a quantum resourceNew Journal of Physics, Vol. 23, No. 8 | 9 August 2021 Cross Ref Quantum Keyless Private Communication Versus Quantum Key Distribution for Space LinksPhysical Review Applied, Vol. 16, No. 1 | 2 July 2021 Cross Ref Quantum Ranging with Gaussian EntanglementPhysical Review Letters, Vol. 126, No. 24 | 14 June 2021 Cross Ref Simple Upper and Lower Bounds on the Ultimate Success Probability for Discriminating Arbitrary Finite-Dimensional Quantum ProcessesPhysical Review Letters, Vol. 126, No. 20 | 18 May 2021 Cross Ref Idler-free channel position findingPhysical Review A, Vol. 103, No. 4 | 29 April 2021 Cross Ref Quantum state discrimination on reconfigurable noise-robust quantum networksPhysical Review Research, Vol. 2, No. 4 | 2 October 2020 Cross Ref Ultimate Limits for Multiple Quantum Channel DiscriminationPhysical Review Letters, Vol. 125, No. 8 | 21 August 2020 Cross Ref Maximal trace distance between isoenergetic bosonic Gaussian statesJournal of Mathematical Physics, Vol. 58, No. 12 | 1 Dec 2017 Cross Ref Nonlocality free wirings and the distinguishability between Bell boxesPhysical Review A, Vol. 95, No. 3 | 17 March 2017 Cross Ref Geometric Measures of Quantum Correlations with Bures and Hellinger DistancesLectures on General Quantum Correlations and their Applications | 25 June 2017 Cross Ref Peculiarities of qubit initial-state preparation by nonselective measurements on an overcomplete basisPhysical Review A, Vol. 92, No. 6 | 9 December 2015 Cross Ref Entropic Lower Bound for Distinguishability of Quantum StatesAdvances in Mathematical Physics, Vol. 2015 | 1 Jan 2015 Cross Ref Iterative methods for finding optimal quantum measurements under minimum-error and minimax criteriaPhysical Review A, Vol. 91, No. 1 | 14 January 2015 Cross Ref Upper bounds on the error probabilities and asymptotic error exponents in quantum multiple state discriminationJournal of Mathematical Physics, Vol. 55, No. 10 | 1 Oct 2014 Cross Ref Quantum correlations and distinguishability of quantum statesJournal of Mathematical Physics, Vol. 55, No. 7 | 1 Jul 2014 Cross Ref Quantum reading of digital memory with non-Gaussian entangled lightPhysical Review A, Vol. 87, No. 5 | 1 May 2013 Cross Ref Quantum state discrimination bounds for finite sample sizeJournal of Mathematical Physics, Vol. 53, No. 12 | 1 Dec 2012 Cross Ref REVERSIBILITY CONDITIONS FOR QUANTUM OPERATIONSReviews in Mathematical Physics, Vol. 24, No. 07 | 1 Aug 2012 Cross Ref Quantum tomography via unambiguous state discriminationPhysical Review A, Vol. 86, No. 1 | 1 July 2012 Cross Ref Achieving the Holevo bound via sequential measurementsPhysical Review A, Vol. 85, No. 1 | 1 January 2012 Cross Ref How Many Copies are Needed for State Discrimination?IEEE Transactions on Information Theory, Vol. 58, No. 1 | 1 Jan 2012 Cross Ref Minimum error discrimination between similarity-transformed quantum statesPhysical Review A, Vol. 84, No. 1 | 1 July 2011 Cross Ref Sequential Projective Measurements for Channel DecodingPhysical Review Letters, Vol. 106, No. 25 | 1 June 2011 Cross Ref Min-entropy and quantum key distribution: Nonzero key rates for "small" numbers of signalsPhysical Review A, Vol. 83, No. 2 | 1 February 2011 Cross Ref Asymptotically Optimal Discrimination between Pure Quantum StatesTheory of Quantum Computation, Communication, and Cryptography | 1 Jan 2011 Cross Ref Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iteratesJournal of Mathematical Physics, Vol. 51, No. 9 | 1 Sep 2010 Cross Ref Exponential error rates in multiple state discrimination on a quantum spin chainJournal of Mathematical Physics, Vol. 51, No. 7 | 1 Jul 2010 Cross Ref Qubit state discriminationPhysical Review A, Vol. 81, No. 6 | 1 June 2010 Cross Ref Discrimination of quantum statesJournal of Modern Optics, Vol. 57, No. 3 | 10 Feb 2010 Cross Ref Optimum unambiguous discrimination of linearly independent pure statesPhysical Review A, Vol. 80, No. 5 | 1 November 2009 Cross Ref Unambiguous modification of nonorthogonal single- and two-photon polarization statesPhysical Review A, Vol. 79, No. 5 | 15 May 2009 Cross Ref Quantum state discriminationAdvances in Optics and Photonics, Vol. 1, No. 2 | 11 February 2009 Cross Ref Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theoremPhysical Review A, Vol. 79, No. 3 | 31 March 2009 Cross Ref Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo–Curlander boundsJournal of Mathematical Physics, Vol. 50, No. 3 | 1 Mar 2009 Cross Ref Asymptotic Error Rates in Quantum Hypothesis TestingCommunications in Mathematical Physics, Vol. 279, No. 1 | 8 February 2008 Cross Ref Quantum Chernoff bound as a measure of distinguishability between density matrices: Application to qubit and Gaussian statesPhysical Review A, Vol. 77, No. 3 | 1 March 2008 Cross Ref Quantum state discrimination and selected applicationsJournal of Physics: Conference Series, Vol. 84 | 12 October 2007 Cross Ref Discriminating States: The Quantum Chernoff BoundPhysical Review Letters, Vol. 98, No. 16 | 1 April 2007 Cross Ref Tomographic quantum cryptographyPhysical Review A, Vol. 68, No. 2 | 1 August 2003 Cross Ref Advances in Quantum DetectionCommunications, Information and Network Security | 1 Jan 2003 Cross Ref Optimal tight frames and quantum measurementIEEE Transactions on Information Theory, Vol. 48, No. 3 | 1 Mar 2002 Cross Ref Reversing quantum dynamics with near-optimal quantum and classical fidelityJournal of Mathematical Physics, Vol. 43, No. 5 | 1 Jan 2002 Cross Ref Optimal phase estimation and square root measurementJournal of Physics A: Mathematical and General, Vol. 34, No. 35 | 24 August 2001 Cross Ref Fidelity and the communication of quantum informationJournal of Physics A: Mathematical and General, Vol. 34, No. 35 | 24 August 2001 Cross Ref Minimum-error discrimination between multiply symmetric statesPhysical Review A, Vol. 64, No. 3 | 1 August 2001 Cross Ref Compression of quantum-measurement operationsPhysical Review A, Vol. 64, No. 1 | 1 June 2001 Cross Ref Quantum channels showing superadditivity in classical capacityPhysical Review A, Vol. 58, No. 1 | 1 July 1998 Cross Ref A demonstration of superadditivity in the classical capacity of a quantum channelPhysics Letters A, Vol. 236, No. 1-2 | 1 Dec 1997 Cross Ref On the design of nonlinear discrete-time predictors (Corresp.)IEEE Transactions on Information Theory, Vol. 28, No. 2 | 1 Mar 1982 Cross Ref Bayes-cost reduction algorithm in quantum hypothesis testing (Corresp.)IEEE Transactions on Information Theory, Vol. 28, No. 2 | 1 Mar 1982 Cross Ref Volume 23, Issue 2| 1979Theory of Probability & Its Applications227-460 History Submitted:22 March 1977Published online:17 July 2006 InformationCopyright © 1979 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1123048Article page range:pp. 411-415ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics