  Quantum-enhanced sensing promises to improve the performance of sensing tasks
using non-classical probes and measurements that require far fewer
scene-modulated photons than the best classical schemes, thereby granting
previously-inaccessible 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 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 and
thereby estimate the desired scene-parameter. The entanglement suppresses the
collective quantum vacuum noise across the phase array. We report simple
analytical expressions for the Cram\'er Rao bound that depend only on the
optical probes and the physical model of the measured system, and we show that
our structured receiver asymptotically saturates the quantum Cram\'er-Rao bound
in the lossless case. Our approach enables Heisenberg limited precision in
estimating a scene-parameter with respect to total probe energy, as well as
with respect to the number of modulated phases. Furthermore, we study the
impact of uniform loss in our system and examine the behavior of both the
quantum and the classical Cram\'er-Rao bounds. We apply our framework to
examples as diverse as radio-frequency phased-array directional radar,
beam-displacement tracking for atomic-force microscopy, and fiber-based
temperature gradiometry.
