Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge

TL;DR

This paper develops a comprehensive framework for optimal quantum phase estimation that incorporates arbitrary prior knowledge, extending beyond traditional Fisher information-based and covariant measurement approaches.

Contribution

It introduces a unified approach to optimal phase estimation considering any level of prior knowledge, analyzing measurement structures, estimators, and probe states.

Findings

Derived the optimal measurement strategies for arbitrary prior knowledge.

Analyzed the structure of optimal probe states and estimators.

Addressed a natural prior distribution from diffusion processes.

Abstract

The optimal phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The structure of the optimal measurements, estimators and the optimal probe states is analyzed. The results fill the gap in the literature on the subject which until now dealt almost exclusively with two extreme cases: almost perfect knowledge (local approach based on Fisher information) and no a priori knowledge (global approach based on covariant measurements). Special attention is paid to a natural a priori probability distribution arising from a diffusion process.