Distributed quantum metrology with a single squeezed-vacuum source

We propose an interferometric scheme for the estimation of a linear combination with non-negative weights of an arbitrary number M > 1 of unknown phase delays, distributed across an M-channel linear optical network, with Heisenberg-limited sensitivity. This is achieved without the need of any sources of photon-number or entangled states, photon-number-resolving detectors, or auxiliary interferometric channels. Indeed, the proposed protocol remarkably relies upon a single squeezed-state source, an antisqueezing operation at the interferometer output, and on-off photodetectors.