Bayesian parameter estimation using Gaussian states and measurements

Bayesian analysis is a framework for parameter estimation that applies even in uncertainty regimes where the commonly used local (frequentist) analysis based on the Cramer-Rao bound (CRB) 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 (CV) 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.

Automated summary

Bayesian analysis provides a framework for parameter estimation that is advantageous in uncertain situations where frequentist analysis may not be well defined. The study examines three paradigmatic estimation schemes in continuous-variable quantum metrology and identifies Bayesian estimation strategies that offer good performance and potential for experimental realization. This research bridges the gap between achievable uncertainties with local estimation techniques and asymptotically optimal strategies.