Machine-Learning-Based Parameter Estimation of Gaussian Quantum States

In this article, we propose a machine-learning framework for parameter estimation of single-mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space displacement and squeezing parameter estimation, this is achieved by introducing expectation–maximization (EM)-based algorithms, while for phase parameter estimation, an empirical Bayes method is applied. The estimated prior distribution parameters along with the observed data are used for finding the optimal Bayesian estimate of the unknown displacement, squeezing, and phase parameters. Our simulation results show that the proposed algorithms have estimation performance that is very close to that of “Genie Aided” Bayesian estimators, which assume perfect knowledge of the prior parameters. In practical scenarios, when numerical values of the prior distribution parameters are not known beforehand, our proposed methods can be used to find optimal Bayesian estimates from the observed measurement data.