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arXiv:2410.07544 · Physical Review A

Entanglement-enhanced Neyman-Pearson target detection

William Ward, Abdulkarim Hariri, Zheshen Zhang

Published Nov 14, 2025• 1 citation
arXivHTMLPDF

Abstract

Quantum illumination (QI) provides entanglement-enabled target detection enhancement, despite operating in an entanglement-breaking environment. Existing experimental studies of QI have utilized a Bayesian approach, assuming that the target is equally likely to be present or absent before detection, to demonstrate an advantage over classical target detection. However, such a premise breaks down in practical operational scenarios in which the prior probability is unknown, thereby hindering QI's applicability to real-world target detection scenarios. In this work, we experimentally implement the phase-conjugate receiver architecture previously envisioned for quantum illumination based target detection, and adopt the Neyman-Pearson criterion in lieu of the error probability for equally likely target absence or presence as our figure of merit for QI. We experimentally demonstrate an unconditional quantum advantage over the optimal classical-illumination protocol as benchmarked by the receiver operating characteristic, which examines detection probability versus false-alarm probability without resorting to known prior probabilities. Our work represents a critical advancement in adapting quantum-enhanced sensing to practical operational settings.

DOI
10.1103/cxl9-ljn8

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Quantum illumination (QI) provides entanglement-enabled target detection enhancement, despite operating in an entanglement-breaking environment. Existing experimental studies of QI have utilized a Bayesian approach, assuming that the target is equally likely to be present or absent before detection, to demonstrate an advantage over classical target detection. However, such a premise breaks down in practical operational scenarios in which the prior probability is unknown, thereby hindering QI's applicability to real-world target detection scenarios. In this work, we experimentally implement the phase-conjugate receiver architecture previously envisioned for quantum illumination based target detection, and adopt the Neyman-Pearson criterion in lieu of the error probability for equally likely target absence or presence as our figure of merit for QI. We experimentally demonstrate an unconditional quantum advantage over the optimal classical-illumination protocol as benchmarked by the receiver operating characteristic, which examines detection probability versus false-alarm probability without resorting to known prior probabilities. Our work represents a critical advancement in adapting quantum-enhanced sensing to practical operational settings.
Quantum illumination (QI) provides entanglement-based target detection—in an entanglement-breaking environment—whose performance is significantly better than that of optimum classical-illumination target detection. QI’s performance advantage was established in a Bayesian setting with the target presumed equally likely to be absent or present and error probability employed as the performance metric. Radar theory, however, eschews that Bayesian approach, preferring the Neyman–Pearson performance criterion to avoid the difficulties of accurately assigning prior probabilities to target absence and presence and appropriate costs to false-alarm and miss errors. We have recently reported an architecture—based on sum-frequency generation (SFG) and feedforward (FF) processing—for minimum error-probability QI target detection with arbitrary prior probabilities for target absence and presence. In this paper, we use our results for FF-SFG reception to determine the receiver operating characteristic—detection probability versus false-alarm probability—for optimum QI target detection under the Neyman–Pearson criterion.
Quantum illumination (QI) is an entanglement-enhanced sensing system whose performance advantage over a comparable classical system survives its usage in an entanglement-breaking scenario plagued by loss and noise. In particular, QI's error-probability exponent for discriminating between equally likely hypotheses of target absence or presence is 6 dB higher than that of the optimum classical system using the same transmitted power. This performance advantage, however, presumes that the target return, when present, has known amplitude and phase, a situation that seldom occurs in light detection and ranging (lidar) applications. At lidar wavelengths, most target surfaces are sufficiently rough that their returns are speckled, i.e., they have Rayleigh-distributed amplitudes and uniformly distributed phases. QI's optical parametric amplifier receiver---which affords a 3 dB better-than-classical error-probability exponent for a return with known amplitude and phase---fails to offer any performance gain for Rayleigh-fading targets. We show that the sum-frequency generation receiver [Zhuang et al., Phys. Rev. Lett. 118, 040801 (2017)]---whose error-probability exponent for a nonfading target achieves QI's full 6 dB advantage over optimum classical operation---outperforms the classical system for Rayleigh-fading targets. In this case, QI's advantage is subexponential: its error probability is lower than the classical system's by a factor of $1/ln(M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B})$, when $M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B}\ensuremath{\gg}1$, with $M\ensuremath{\gg}1$ being the QI transmitter's time-bandwidth product, ${N}_{S}\ensuremath{\ll}1$ its brightness, $\overline{\ensuremath{\kappa}}$ the target return's average intensity, and NB{N}_{B}NB​ the background light's brightness.
Quantum illumination utilizes an entanglement-enhanced sensing system to outperform classical illumination in detecting a suspected target, despite the entanglement-breaking loss and noise. However, practical and optimal receiver design to fulfill the quantum advantage has been a long open problem. Recently, Shi et al. [arXiv:2207.06609 (2022)] proposed the correlation-to-displacement $(`\mathrm{C}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}_{\stackrel{P\vec}{}}\phantom{\rule{0.16em}{0ex}}\mathrm{D}\text{'})$ conversion module to enable an optimal receiver design that greatly reduces the complexity of the previous known optimal receiver [Q. Zhuang, Z. Zhang, and J. H. Shapiro, Phys. Rev. Lett. 118, 040801 (2017)]. There, the analyses of the conversion module assume an ideal target with a known reflectivity and a fixed return phase. In practical applications, however, targets often induce a random return phase; moreover, their reflectivities can have fluctuations obeying a Rayleigh distribution. In this paper, we extend the analyses of the $\mathrm{C}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}_{\stackrel{P\vec}{}}\phantom{\rule{0.16em}{0ex}}\mathrm{D}$ module to realistic targets and show that the entanglement advantage is maintained albeit reduced. In particular, the conversion module allows exact and efficient performance evaluation despite the non-Gaussian nature of the quantum channel involved.
Quantum target detection is an emerging application that utilizes entanglement to enhance the sensing of the presence of an object. Although several experimental demonstrations for certain situations have been reported recently, the single-shot detection limit imposed by the Helstrom limit has not been reached because of the unknown optimum measurements. Here we report an experimental demonstration of quantum target detection, also known as quantum illumination, in the single-photon limit. In our experiment, one photon of the maximally entangled photon pair is employed as the probe signal and the corresponding optimum measurement is implemented at the receiver. We explore the detection problem in different regions of the parameter space and verify that the quantum advantage exists even in a forbidden region of the conventional illumination, where all classical schemes become useless. Our results indicate that quantum illumination breaks the classical limit for up to 40%, while approaching the quantum limit imposed by the Helstrom limit. These results not only demonstrate the advantage of quantum illumination, but also manifest its valuable potential of target detection.
Quantum illumination (QI) is the task of querying a scene using a transmitter probe whose quantum state is entangled with a reference beam retained in ideal storage, followed by optimally detecting the target-returned light together with the stored reference, to make decisions on characteristics of targets at stand-off range, at precision that exceeds what is achievable with a classical transmitter of the same brightness and otherwise identical conditions. Using tools from perturbation theory, we show that in the limit of low transmitter brightness, high loss, and high thermal background, there is a factor of four improvement in the Chernoff exponent of the error probability in discriminating any number of apriori-known reflective targets when using a Gaussian-state entangled QI probe, over using classical coherent-state illumination (CI). While this advantage was known for detecting the presence or absence of a target, it had not been proven for the generalized task of discriminating between arbitrary target libraries. In proving our result, we derive simple general analytic expressions for the lowest-order asymptotic expansions of the quantum Chernoff exponents for QI and CI in terms of the signal brightness, loss, thermal noise, and the modal expansion coefficients of the target-reflected light's radiant exitance profiles when separated by a spatial mode sorter after entering the entrance pupil of the receiver's aperture.
Quantum-enhanced sensing has a goal of enhancing a parameter sensitivity with input quantum states, while quantum illumination has a goal of enhancing a target detection capability with input entangled states in a heavy noise environment. Here we propose a concatenation between quantum-enhanced sensing and quantum illumination that can take quantum advantage over the classical limit. First, phase sensing in an interferometry is connected to a target sensing via quantum Fisher information. Second, the target sensitivity is investigated in noisy quantum-enhanced sensing. Under the same input state energy, for example, NNN-photon entangled states can exhibit better performance than a two-mode squeezed vacuum state and a separable coherent state. Incorporating a photon-number difference measurement, finally, the noisy target sensitivity is connected to a signal-to-noise ratio which is associated with a minimum error probability of discriminating the presence and absence of the target. We show that both the target sensitivity and the signal-to-noise ratio can be enhanced with increasing thermal noise.