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.
Highlights
High precision measurements of physical quantities are of fundamental importance in all branches of physics and beyond
Our scheme is by construction blind to signals with a different spatial dependence than the signal of interest, and insensitive to noise coming from fluctuations of these quantities
In this work we have introduced general sensing schemes to directly measure a given quantity of interest with a certain spatial distribution
Summary
High precision measurements of physical quantities are of fundamental importance in all branches of physics and beyond. The quantity of interest is not a local property, but has a characteristic spatial dependence such as, e.g., the gradient (or higher moment) of a field, or a (spatial) Fourier coefficient In this case, multiple measurements performed at different positions are required, i.e., one uses distributed sensors or sensor networks. Our scheme is by construction blind to signals with a different spatial dependence than the signal of interest, and insensitive to noise coming from fluctuations of these quantities This is possible due to the additional freedom of placing sensors at arbitrary positions, and implies for example that gradients can be sensed despite arbitrarily large fluctuations of the global field. In a real world application other noise mechanisms are present and have to be addressed independently
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