A robust Bayesian formulation of the optimal phase measurement problem

TL;DR

This paper introduces a Bayesian approach to optimize quantum-limited optical phase measurements, addressing complex distribution pathologies and providing a robust framework for performance bounds in metrology applications.

Contribution

It reformulates the optimal phase measurement problem within a Bayesian framework using Shannon information, enabling robust bounds without relying on the central limit theorem.

Findings

Single-mode performance bounds derived

Multi-mode bounds reduced to a single integral

Robust statistical methods developed for quantum measurements

Abstract

Optical phase measurement is a simple example of a quantum--limited measurement problem with important applications in metrology such as gravitational wave detection. The formulation of optimal strategies for such measurements is an important test-bed for the development of robust statistical methods for instrument evaluation. However, the class of possible distributions exhibits extreme pathologies not commonly encountered in conventional statistical analysis. To overcome these difficulties we reformulate the basic variational problem of optimal phase measurement within a Bayesian paradigm and employ the Shannon information as a robust figure of merit. Single-mode performance bounds are discussed, and we invoke a general theorem that reduces the problem of finding the multi-mode performance bounds to the bounding of a single integral, without need of the central limit theorem.