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Explicit-duration Hidden Markov Models for quantum state estimation

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  • Luati, Alessandra
  • Novelli, Marco

Abstract

An explicit-duration Hidden Markov Model with a nonparametric kernel estimator of the state duration distribution is specified. The motivation comes from the physical problem of extracting the maximum information from an open quantum system subject to an external perturbation, which induces a change in the dynamics of the system. A nonparametric kernel estimator for discrete data is introduced, which is consistent and improves the estimates accuracy in presence of sparse data. To reconstruct the hidden dynamics, a Viterbi algorithm is used, which is robust against the underflow problem. Finite sample properties are investigated through an extensive Monte Carlo study showing that our formulation outperforms the original one both in small and in large samples.

Suggested Citation

  • Luati, Alessandra & Novelli, Marco, 2021. "Explicit-duration Hidden Markov Models for quantum state estimation," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:csdana:v:158:y:2021:i:c:s0167947321000177
    DOI: 10.1016/j.csda.2021.107183
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    References listed on IDEAS

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    1. 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.
    2. Bulla, Jan & Bulla, Ingo, 2006. "Stylized facts of financial time series and hidden semi-Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2192-2209, December.
    3. James M McFarland & Thomas T G Hahn & Mayank R Mehta, 2011. "Explicit-Duration Hidden Markov Model Inference of UP-DOWN States from Continuous Signals," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-16, June.
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