Joint estimation of phase and phase diffusion for quantum metrology

TL;DR

This paper derives fundamental limits and optimal measurement strategies for jointly estimating phase and phase diffusion in quantum systems, crucial for improving quantum metrology under noise.

Contribution

It introduces a quantum limit for joint phase and diffusion estimation and provides optimal measurement schemes for relevant quantum states.

Findings

Derived a trade-off bound on variances for joint estimation

Identified optimal measurement schemes for specific quantum states

Quantified effectiveness using an experimental polarimetry setup

Abstract

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here, we investigate the joint estimation of a phase shift and the amplitude of phase diffusion, at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states -- split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental setup for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.