Markov Chain Monte Carlo Estimation of Quantum States

TL;DR

This paper introduces a Bayesian MCMC approach for quantum state tomography, providing comprehensive statistical information and uncertainties, demonstrated on non-Gaussian phase-diffused squeezed states, and compared with traditional methods.

Contribution

The paper presents a novel application of MCMC for quantum state reconstruction that captures full statistical correlations without prior distribution assumptions.

Findings

MCMC yields detailed statistical distributions of quantum state parameters.

The method successfully reconstructs non-Gaussian states like phase-diffused squeezed states.

Results are comparable or superior to maximum-likelihood and Fisher information approaches.

Abstract

We apply a Bayesian data analysis scheme known as the Markov Chain Monte Carlo (MCMC) to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector can be derived, e. g. the marginal distributions and uncertainties of all model parameters and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states posses non-Gaussian statistics and therefore represent a non-trivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.