Bayesian nonparametric estimation for Quantum Homodyne Tomography
Résumé
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.
Mots clés
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
and phrases: Bayesian nonparametric estimation
inverse prob- lem
rate of con- traction
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OpenAccess_ZacharieNaulet_euclid.ejs.1507255615.pdf (1.21 Mo)
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