# Optimal distributed sensing in noisy environments

## TL;DR

This paper introduces quantum-enhanced distributed sensing protocols that achieve optimal measurement precision for spatially dependent fields, demonstrating exponential advantages over classical strategies in noisy environments.

## Contribution

It presents a novel quantum sensing scheme with optimal Heisenberg scaling, unaffected by certain noise, for measuring non-local spatial quantities using entangled states.

## Key findings

- Achieves Heisenberg-limited scaling in noisy environments
- Demonstrates exponential advantage over classical methods
- Provides explicit measurement strategies for spatial series coefficients

## Abstract

We consider distributed sensing of non-local quantities. We introduce quantum enhanced protocols to directly measure any (scalar) field with a specific spatial dependence by placing sensors at appropriate positions and preparing a spatially distributed entangled quantum state. Our scheme has optimal Heisenberg scaling and is completely unaffected by noise on other processes with different spatial dependence than the signal. We consider both Fisher and Bayesian scenarios, and design states and settings to achieve optimal scaling. We explicitly demonstrate how to measure coefficients of spatial Taylor and Fourier series, and show that our approach can offer an exponential advantage as compared to strategies that do not make use of entanglement between different sites.