Explicit-duration Hidden Markov Models for quantum state estimation

Alessandra Luati and Marco Novelli

Computational Statistics & Data Analysis, 2021, vol. 158, issue C

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.

Keywords: Hidden Markov Models; Forward–backward algorithm; Quantum statistics; Kernel estimation; Viterbi algorithm (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:158:y:2021:i:c:s0167947321000177

DOI: 10.1016/j.csda.2021.107183

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