Bayesian estimation in homodyne interferometry

TL;DR

This paper investigates Bayesian phase estimation using squeezed vacuum and homodyne detection, proposing adaptive methods to optimize measurement precision and approach quantum limits.

Contribution

It introduces two feasible adaptive strategies for optimizing homodyne detection in phase estimation, enhancing precision near quantum bounds.

Findings

Bayesian estimator asymptotically reaches the Cramer-Rao bound.

Adaptive methods improve measurement precision with few data points.

Monte Carlo simulations validate the effectiveness of the proposed strategies.

Abstract

We address phase-shift estimation by means of squeezed vacuum probe and homodyne detection. We analyze Bayesian estimator, which is known to asymptotically saturate the classical Cramer-Rao bound to the variance, and discuss convergence looking at the a posteriori distribution as the number of measurements increases. We also suggest two feasible adaptive methods, acting on the squeezing parameter and/or the homodyne local oscillator phase, which allow to optimize homodyne detection and approach the ultimate bound to precision imposed by the quantum Cramer-Rao theorem. The performances of our two-step methods are investigated by means of Monte Carlo simulated experiments with a small number of homodyne data, thus giving a quantitative meaning to the notion of asymptotic optimality.