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arXiv:1706.05561 · Physical Review A

Quantum illumination for enhanced detection of Rayleigh-fading targets

Quntao Zhuang, Zheshen Zhang, Jeffrey H. Shapiro

Published Aug 15, 2017• 51 citations
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Abstract

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 ${N}_{B}$ the background light's brightness.

DOI
10.1103/physreva.96.020302

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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\ensuremathκ‾NS/NB)1/ln(M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B})1/ln(M\ensuremathκ​NS​/NB​), when M\ensuremathκ‾NS/NB\ensuremath≫1M\overline{\ensuremath{\kappa}}{N}_{S}/{N}_{B}\ensuremath{\gg}1M\ensuremathκ​NS​/NB​\ensuremath≫1, with M\ensuremath≫1M\ensuremath{\gg}1M\ensuremath≫1 being the QI transmitter's time-bandwidth product, NS\ensuremath≪1{N}_{S}\ensuremath{\ll}1NS​\ensuremath≪1 its brightness, \ensuremathκ‾\overline{\ensuremath{\kappa}}\ensuremathκ​ 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 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-based protocol for improving LiDAR/radar detection of unresolved targets beyond what a classical LiDAR/radar of the same average transmitted energy can do. Originally proposed by Seth Lloyd as a discrete-variable quantum LiDAR, it was soon shown that his proposal offered no quantum advantage over its best classical competitor. Continuous-variable, specifically Gaussian-state, QI has been shown to offer a true quantum advantage, both in theory and in table-top experiments. Moreover, despite its considerable drawbacks, the microwave version of Gaussian-state QI continues to attract research attention. A recent QI study by Armanpreet Pannu, Amr Helmy, and Hesham El Gamal (PHE), however, has: (i) combined the entangled state from Lloyd’s QI with the channel models from Gaussian-state QI; (ii) proposed a new positive operator-valued measurement for that composite setup; and (iii) claimed that, unlike Gaussian-state QI, PHE QI achieves the Nair–Gu lower bound on QI target-detection error probability at all noise brightnesses. PHE’s analysis was asymptotic, i.e., it presumed infinite-dimensional entanglement. The current paper works out the finite-dimensional performance of PHE QI. It shows that there is a threshold value for the entangled-state dimensionality below which there is no quantum advantage, and above which the Nair–Gu bound is approached asymptotically. Moreover, with both systems operating with error-probability exponents 1 dB lower than the Nair–Gu bound, PHE QI requires enormously higher entangled-state dimensionality than does Gaussian-state QI to achieve useful error probabilities in both high-brightness (100 photons/mode) and moderate-brightness (1 photon/mode) noise. Furthermore, neither system has an appreciable quantum advantage in low-brightness (much less than 1 photon/mode) noise.
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) 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.
In quantum illumination (QI), a signal beam initially entangled with an idler beam held at the receiver interrogates a target region bathed in thermal background light. The returned beam is measured jointly with the idler in order to determine whether a weakly reflecting target is present. Using tools from quantum information theory, we derive lower bounds on the average error probability of detecting both specular and fading targets and on the mean squared error of estimating the reflectance of a detected target, which are obeyed by any QI transmitter satisfying a signal energy constraint. For bright thermal backgrounds, we show that the QI system using multiple copies of low-brightness two-mode squeezed vacuum states is nearly optimal. More generally, our results place limits on the best possible performance achievable using QI systems at all wavelengths, and at all signal and background noise levels.