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
- rate of con- traction
- Bayesian nonparametric estimation
- inverse problem
- nonparametric estimation
- quantum homodyne tomography
- Radon transform
- Wigner distribution
- mixture prior
- inverse prob- lem
- and phrases: Bayesian nonparametric estimation
- MINIMAX
- WIGNER FUNCTION
- MODULATION SPACES
- CONVERGENCE-RATES
- POSTERIOR DISTRIBUTIONS
- NOISY DATA
- rate of contraction
- Wilson bases
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