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Abstract
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.
Highlights
Quantum phenomena are known to be powerful and viable tools to enhance estimation precision in diverse fields, e.g., astronomy [1], general relativity [2,3,4,5], models for quantum-to-classical transition [6], microscopy [7], and optical imaging [8,9,10]
We proved a Heisenberg limited scaling of the Fisher Information Ix = O(N2) in estimating the parameter in terms of the total photon-unit energy N employed by the sensor
Additional constant factor improvements in Ix are possible over our simple receiver design, e.g., by optimizing UI for known functions θm(x)
Summary
Quantum phenomena are known to be powerful and viable tools to enhance estimation precision in diverse fields, e.g., astronomy [1], general relativity [2,3,4,5], models for quantum-to-classical transition [6], microscopy [7], and optical imaging [8,9,10]. In an idealized sensing context, this improvement takes the form of an improved scaling of estimation variance with probe power, known as Heisenberg scaling This Heisenberg scaling for sensitivity can be obtained using Gaussian quantum states of light (that can be generated using lasers, linear optics, and squeezed light, e.g., produced using parametric amplifiers) and Gaussian measurements (i.e., homodyne and heterodyne detection). One widely applicable scenario for distributed quantum sensing is as follows: a quantitative parameter of interest x modulates a series of M optical phase delays in M optical modes with nonsymmetric but known functional relationships to the parameter, and the parameter must be estimated using user-controlled probes and measurements This problem statement can be used to model various practical photonic sensing tasks, some specific examples of which have been recently studied. Applications of our model reach beyond photonic sensors, and could serve as the foundation for more general distributed quantum sensing tasks with applications to quantum process tomography of quantum computers and quantum network tomography
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