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Bayesian nonparametric estimation for Quantum Homodyne Tomography

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Date
2017
Dewey
Traitement du signal
Sujet
Bayesian nonparametric estimation; inverse problem; nonparametric estimation; quantum homodyne tomography; Radon transform; Wigner distribution; mixture prior; Wilson bases; rate of contraction; Noisy data; Posterior distributions; Convergence-rates; Modulation spaces; Wigner function; Minimax
Journal issue
Electronic Journal of Statistics
Volume
11
Number
2
Publication date
2017
Article pages
3595 - 3632
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/17-EJS1322
URI
https://basepub.dauphine.fr/handle/123456789/18379
Collections
  • CEREMADE : Publications
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Author
Naulet, Zacharie
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Barat, Éric
40217 Laboratoire d'Intégration des Systèmes et des Technologies [LIST]
Type
Article accepté pour publication ou publié
Abstract (EN)
We estimate the quantum state of a light beam from results of quantum homodyne tomography noisy measurements performed on identically prepared quantum systems. We propose two Bayesian nonparametric approaches. The first approach is based on mixture models and is illustrated through simulation examples. The second approach is based on random basis expansions. We study the theoretical performance of the second approach by quantifying the rate of contraction of the posterior distribution around the true quantum state in the L-2 metric.

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