Abstract
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.
Highlights
Q UANTUM metrology is one of the important quantum technologies that uses quantum mechanics to study the ultimate limits with which physical quantities can be estimated [1], [2]
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
We have proposed machine learning based methods for parameter estimation of continuous variable Gaussian quantum states
Summary
Q UANTUM metrology is one of the important quantum technologies that uses quantum mechanics to study the ultimate limits with which physical quantities can be estimated [1], [2]. We propose a machine learning based method for three important estimation problems for Gaussian states: (i) phase-space displacement estimation, (ii) single-mode squeezing parameter estimation, and (iii) phase estimation This problem has recently been studied in [8], where authors have proposed Bayesian estimation schemes. This multiple measurement scenario has been considered by recent works on data driven quantum information processing, where authors have proposed machine learning based Hamiltonian estimation [27], single electron Rabi frequency estimation [23], single qubit rotation estimation [24], and machine learning based quantum interferometry [26] In this regard, our proposed machine learning based method is a hybrid method combining both Bayesian and frequentist approaches for estimating the unknown parameters. We focus on single mode Gaussian quantum states and propose a machine learning based method to estimate the prior distribution parameters from the observed measurement data.
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