Entanglement enhanced estimation of parameter embedded in multiple phases

Quantum enhanced sensing promises to improve the performance of sensing tasks using non-classical probes and measurements using far less scene-modulated photons than possible by the best classical scheme, thereby gaining previously-inaccessible quantitative information about a wide range of physical systems. We propose a generalized distributed sensing framework that uses an entangled quantum probe to estimate a scene-parameter that is encoded within an array of phases, with a functional dependence on that parameter determined by the physics of the actual system. The receiver uses a laser light source enhanced by quantum-entangled multi-partite squeezed-vacuum light to probe the phases, to estimate the desired scene parameter. The entanglement suppresses the collective quantum vacuum noise across the phase array. We show our approach enables Heisenberg limited sensitivity in estimating the scene parameter with respect to total probe energy, as well as with respect to the number of modulated phases, and saturates the quantum Cramer Rao bound. We apply our approach to examples as diverse as radio-frequency phased-array directional radar, fiber-based temperature gradiometer, and beam-displacement tracking for atomic-force microscopy.