Distributed quantum sensing and entanglement-enhanced multiphase estimation theory

We study a phase estimation protocol based on the distribution of a single squeezed state among an array of Mach-Zehnder interferometers (MZIs). The fundamental component of our scheme is the quantum circuit (QC), a linear network that optimally distributes the squeezing generated at one of its inputs among the d MZIs, where d unknown parameters θ1, . . . , θd are then imprinted and the number of photons at the outputs finally measured. For any given linear combination of the parameters, we can optimize the QC and achieve sub-shot-noise sensitivity. Our parallel strategy, based on the mode-entanglement created by the QC, outperforms the rival and more common sequential strategy, in which the same unknown parameters are estimated independently. It also saturates the ultimate sensitivity bound, the quantum Cramer-Rao bound, in a relevant regime of parameters, thus constituting an optimal estimation method in that regime.