Bayesian nonparametric estimation for Quantum Homodyne Tomography

TL;DR

This paper introduces two Bayesian nonparametric methods for estimating quantum states from noisy homodyne tomography data, providing theoretical analysis and simulation validation for improved quantum state reconstruction.

Contribution

It presents novel Bayesian nonparametric approaches for quantum state estimation, including mixture models and random basis expansions, with theoretical performance analysis.

Findings

The second approach achieves quantifiable posterior contraction rates.

Simulation examples demonstrate the effectiveness of the proposed methods.

Theoretical analysis confirms the convergence properties of the second approach.

Abstract

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.