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On quantum statistical inference

Author

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  • Ole E. Barndorff‐Nielsen
  • Richard D. Gill
  • Peter E. Jupp

Abstract

Summary. Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems. Furthermore, developments in the theory of quantum measurements have brought the basic mathematical framework for the probability calculations much closer to that of classical probability theory. The present paper reviews this field and proposes and interrelates some new concepts for an extension of classical statistical inference to the quantum context.

Suggested Citation

  • Ole E. Barndorff‐Nielsen & Richard D. Gill & Peter E. Jupp, 2003. "On quantum statistical inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 775-804, November.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:4:p:775-804
    DOI: 10.1111/1467-9868.00415
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    Cited by:

    1. Jupp, P.E., 2010. "A van Trees inequality for estimators on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1814-1825, September.
    2. Luati, Alessandra & Novelli, Marco, 2020. "The Hammersley–Chapman–Robbins inequality for repeatedly monitored quantum system," Statistics & Probability Letters, Elsevier, vol. 165(C).
    3. Eric Ghysels & Jack Morgan, 2024. "On Quantum Ambiguity and Potential Exponential Computational Speed-Ups to Solving Dynamic Asset Pricing Models," Papers 2405.01479, arXiv.org, revised May 2024.
    4. Heller, B. & Wang, M., 2007. "Posterior distribution for negative binomial parameter p using a group invariant prior," Statistics & Probability Letters, Elsevier, vol. 77(15), pages 1542-1548, September.
    5. Vladislav Kargin, 2004. "Coordination Games with Quantum Information," Game Theory and Information 0409006, University Library of Munich, Germany.
    6. Dale, M.B. & Dale, P.E.R. & Tan, P., 2007. "Supervised clustering using decision trees and decision graphs: An ecological comparison," Ecological Modelling, Elsevier, vol. 204(1), pages 70-78.
    7. Luati, Alessandra & Novelli, Marco, 2021. "Explicit-duration Hidden Markov Models for quantum state estimation," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    8. Jamal Anwar, S. & Ramzan, M. & Usman, M. & Khalid Khan, M., 2020. "Thermal and intrinsic decoherence effects on the dynamics of two three-level moving atomic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).

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