Explicit-duration Hidden Markov Models for quantum state estimation

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...

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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 158; p. 107183
Main Authors: Luati, Alessandra, Novelli, Marco
Format: Journal Article
Language:English
Published: Elsevier B.V 01.06.2021
Subjects:
algorithms
data analysis
Forward–backward algorithm
Hidden Markov Models
Kernel estimation
Markov chain
Monte Carlo method
motivation
Quantum statistics
Viterbi algorithm
Kernel estimation
Viterbi algorithm
Hidden Markov Models
Forward–backward algorithm
Quantum statistics
ISSN:0167-9473, 1872-7352
Online Access:Get full text
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Summary: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.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2021.107183