Bayesian estimation in homodyne interferometry

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.

12 pages, 5 figures, published version

References in corpus (3)

• Optimal quantum estimation of loss in bosonic channels
• Optimal phase measurements with pure Gaussian states
• Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry