Multi-parameter estimation in networked quantum sensors

TL;DR

This paper establishes that for many quantum sensor network estimation tasks, entanglement and global measurements offer limited advantage, with separable states often achieving optimal precision, except for global property estimations.

Contribution

The paper provides rigorous theorems demonstrating when entanglement and global measurements improve quantum sensor network estimations, clarifying their limited benefits in many scenarios.

Findings

Separable states often achieve the quantum limit in parameter estimation.

Entanglement provides advantages mainly for global network properties.

Local measurements are optimal for many multi-parameter estimation problems.

Abstract

We introduce a general model for a network of quantum sensors, and we use this model to consider the question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or non-linear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.