Optimality of Gaussian receivers for practical Gaussian distributed sensing

TL;DR

This paper investigates the optimal measurement strategies for estimating spatial parameters using Gaussian distributed sensors and demonstrates that Gaussian, separable measurements are optimal under practical conditions, with adaptive techniques enhancing robustness.

Contribution

It proves that Gaussian, separable measurements are locally optimal for phase estimation in a practical sensing setup, and explores the benefits of structured entangling receivers.

Findings

Gaussian measurements achieve the standard quantum limit.

Separable measurements are optimal for the considered setting.

Adaptive phase measurements improve robustness with limited prior information.

Abstract

We study the problem of estimating a function of many parameters acquired by sensors that are distributed in space, e.g., the spatial gradient of a field. We restrict ourselves to a setting where the distributed sensors are probed with experimentally practical resources, namely, field modes in separable displaced thermal states, and focus on the optimal design of the optical receiver that measures the phase-shifted returning field modes. Within this setting, we demonstrate that a locally optimal measurement strategy, i.e., one that achieves the standard quantum limit for all phase shift values, is a Gaussian measurement, and moreover, one that is separable. We also demonstrate the utility of adaptive phase measurements for making estimation performance robust in cases where one has little prior information on the unknown parameters. In this setting we identify a regime where it is beneficial to use structured optical receivers that entangle the received modes before measurement.