Open Access
2017 Bayesian nonparametric estimation for Quantum Homodyne Tomography
Zacharie Naulet, Éric Barat
Electron. J. Statist. 11(2): 3595-3632 (2017). DOI: 10.1214/17-EJS1322


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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Zacharie Naulet. Éric Barat. "Bayesian nonparametric estimation for Quantum Homodyne Tomography." Electron. J. Statist. 11 (2) 3595 - 3632, 2017.


Received: 1 October 2016; Published: 2017
First available in Project Euclid: 6 October 2017

zbMATH: 1373.62136
MathSciNet: MR3709864
Digital Object Identifier: 10.1214/17-EJS1322

Primary: 62G05
Secondary: 62G20 , 81V80

Keywords: Bayesian nonparametric estimation , inverse problem , mixture prior , nonparametric estimation , quantum homodyne tomography , Radon transform , rate of contraction , Wigner distribution , Wilson bases

Vol.11 • No. 2 • 2017
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