Frequentist and Bayesian Quantum Phase Estimation

TL;DR

This paper compares frequentist and Bayesian quantum phase estimation methods, highlighting their conceptual differences, limitations, and the applicability of their sensitivity bounds in quantum noise-limited interferometry.

Contribution

It provides a detailed comparison of the two frameworks and clarifies the applicability of their bounds to fixed and fluctuating phase parameters.

Findings

Frequentist and Bayesian bounds are not interchangeable.

Bounds for fluctuating parameters do not apply to fixed parameters.

The paper clarifies the conceptual differences between the two approaches.

Abstract

Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cram\`er-Rao bound, for instance, do not apply to Bayesian strategies and vice-versa. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter.