Bayesian parameter estimation using Gaussian states and measurements

TL;DR

This paper explores Bayesian parameter estimation in continuous-variable quantum metrology, demonstrating strategies with Gaussian states and measurements that improve precision in regimes where traditional methods are inadequate.

Contribution

It introduces Bayesian analysis to quantum metrology scenarios, identifying practical Gaussian-based strategies for high-precision parameter estimation in low-information regimes.

Findings

Bayesian methods outperform local techniques in uncertain regimes

Gaussian states and measurements enable practical high-precision estimation

Strategies bridge the gap to asymptotically optimal estimation

Abstract

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cram\'er-Rao bound is not well defined. In particular, it applies when no initial information about the parameter value is available, e.g., when few measurements are performed. Here, we consider three paradigmatic estimation schemes in continuous-variable quantum metrology (estimation of displacements, phases, and squeezing strengths) and analyse them from the Bayesian perspective. For each of these scenarios, we investigate the precision achievable with single-mode Gaussian states under homodyne and heterodyne detection. This allows us to identify Bayesian estimation strategies that combine good performance with the potential for straightforward experimental realization in terms of Gaussian states and measurements. Our results provide practical solutions for reaching uncertainties where local estimation techniques apply, thus bridging the gap to regimes where asymptotically optimal strategies can be employed.