Abstract
Proofs of the quantum advantage available in imaging or detecting objects under quantum illumination can rely on optimal measurements without specifying what they are. We use the continuous-variable Gaussian quantum information formalism to show that quantum illumination is better for object detection compared with coherent states of the same mean photon number, even for simple direct photodetection. The advantage persists if signal energy and object reflectivity are low and background thermal noise is high. The advantage is even greater if we match signal beam detection probabilities rather than mean photon number. We perform all calculations with thermal states, even for non-Gaussian conditioned states with negative Wigner functions. We simulate repeated detection using a Monte-Carlo process that clearly shows the advantages obtainable.
Highlights
Quantum states of light for object detection in a noisy environment, coined as “quantum illumination”, were originally introduced [1] and subsequently investigated for continuous variable Gaussian states [2,3,4] - states with Gaussian Wigner functions
In this paper we have described a theory of quantum illumination for target detection in a noisy background
Our theory is written in terms of the the formalism of Gaussian quantum optics and can be wholly characterized using thermal Gaussian states, even in cases where the heralded state has a negative Wigner function and cannot be written as a Gaussian state
Summary
Quantum states of light for object detection in a noisy environment, coined as “quantum illumination”, were originally introduced [1] and subsequently investigated for continuous variable Gaussian states [2,3,4] - states with Gaussian Wigner functions. Quantum illumination uses quantum correlations to provide improved object detection when compared to classical light sources The proof of this advantage, at optical frequencies or in quantum radar signal discrimination, boils down to an optimization problem focused on minimizing the probability of error in hypothesis testing; from thereon parameters are chosen to present a favourable picture where quantum states gain a performance advantage over illumination with coherent states. Since this is a statistical analysis of QI, it is frequency independent and could be applied both to lidar and to radar By employing this simple click detection strategy, we can calculate the click probability of the return signal after its interaction with an external object, whilst incorporating any associated quantum efficiencies and thermal background noise sources, including detector dark counts.
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