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The Hammersley–Chapman–Robbins inequality for repeatedly monitored quantum system

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  • Luati, Alessandra
  • Novelli, Marco

Abstract

We derive the Hammersley–Chapman–Robbins inequality for discrete quantum parameter models in the presence of time dependent measurements. The extension determines a discrete counterpart of the classical Fisher information. We provide an illustration concerning a quantum optics problem.

Suggested Citation

  • Luati, Alessandra & Novelli, Marco, 2020. "The Hammersley–Chapman–Robbins inequality for repeatedly monitored quantum system," Statistics & Probability Letters, Elsevier, vol. 165(C).
    • Handle: RePEc:eee:stapro:v:165:y:2020:i:c:s0167715220301553
    DOI: 10.1016/j.spl.2020.108852
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    References listed on IDEAS

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    1. LaMotte, Lynn Roy, 2008. "Sufficiency in Finite Parameter and Sample Spaces," The American Statistician, American Statistical Association, vol. 62, pages 211-215, August.
    2. Christine Choirat & Raffaello Seri, 2001. "Estimation in Discrete Parameter Models," Working Papers 2001-38, Center for Research in Economics and Statistics.
    3. Rasul A. Khan, 2003. "A note on Hammersley's inequality for estimating the normal integer mean," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-10, January.
    4. 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.
    5. Julio T. Barreiro & Markus Müller & Philipp Schindler & Daniel Nigg & Thomas Monz & Michael Chwalla & Markus Hennrich & Christian F. Roos & Peter Zoller & Rainer Blatt, 2011. "An open-system quantum simulator with trapped ions," Nature, Nature, vol. 470(7335), pages 486-491, February.
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