Distributed quantum sensing with squeezed-vacuum light in a configurable array of Mach-Zehnder interferometers

We study an entangled distributed quantum sensing scheme based on an array of d Mach-Zehnder interferometers (MZIs) for the estimation of relative phase shifts. The scheme uses d coherent states and a single squeezed-vacuum state that is distributed among the MZIs by a quantum circuit (QC). The protocol can be optimized analytically: it overcomes the shot-noise limit and reaches the Heisenberg limit with respect to the average total number of probe particles, n(T) , for the estimation of arbitrary linear combinations of the d phases. We compare the entangled strategy with a separable one that uses d coherent and d squeezed-vacuum states and the same n(T) . The entangled strategy benefits for a substantial reduction of resource overhead and can achieve a maximum gain equal to d when using the same total squeezed-light intensity as the separable strategy. Interestingly, the entangled strategy using a single squeezed-vacuum state can reach the same sensitivity as the separable strategy that uses d copies of the same state. Finally, given a random choices of the QC, we identify the optimal linear combination of the phases that can be estimated with maximum sensitivity. Our scheme paves the ways for a variety of applications in distributed quantum sensing with photonic and atomic interferometers.