Optimal distributed sensing in noisy environments

Abstract

We consider distributed sensing of nonlocal 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 filters out noise with different spatial dependence than the signal. We provide states, spatial sensor configurations, and protocols 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.