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Physical Review A

Machine-learning-aided direct estimation of coherence and entanglement for unknown states

Ting Lin, Zhihua Chen, Kai Wu, Zhihua Guo, Zhihao Ma, Shao-Ming Fei

Published Dec 15, 2025• 0 citations
Publisher
DOI
10.1103/958b-87zr

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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, that 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.
Abstract Quantifying entanglement measures for quantum states with unknown density matrices is a challenging task. Machine learning offers a new perspective to address this problem. By training machine learning models using experimentally measurable data, we can predict the target entanglement measures. In this study, we compare various machine learning models and find that the linear regression and stack models perform better than others. We investigate the model’s impact on quantum states across different dimensions and find that higher-dimensional quantum states yield better results. Additionally, we investigate which measurable data has better predictive power for target entanglement measures. Using correlation analysis and principal component analysis, we demonstrate that quantum moments exhibit a stronger correlation with coherent information among these data features.