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arXiv:2212.08190 · Physical Review A

Entanglement-assisted detection of fading targets via correlation-to-displacement conversion

Xin Chen, Quntao Zhuang

Published Jun 5, 2023• 6 citations
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Abstract

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.

DOI
10.1103/physreva.107.062405

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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) 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.
Entanglement is vulnerable to degradation in a noisy sensing scenario, but surprisingly, the quantum illumination protocol has demonstrated that its advantage can survive. However, designing a measurement system that realizes this advantage is challenging since the information is hidden in the weak correlation embedded in the noise at the receiver side. Recent progress in a correlation-to-displacement conversion module provides a route towards an optimal protocol for practical microwave quantum illumination. In this work, we extend the conversion module to accommodate experimental imperfections that are ubiquitous in microwave systems. To mitigate loss, we propose amplification of the return signals. In the case of ideal amplification, the entire six-decibel error-exponent advantage in target detection error can be maintained. However, in the case of noisy amplification, this advantage is reduced to three decibels. We analyze the quantum advantage under different scenarios with a Kennedy receiver in the final measurement. In the ideal case, the performance still achieves the optimal one over a fairly large range of error probability with only on-off detection. Empowered by photon-number-resolving detectors, the performance is further improved and also analyzed in terms of receiver operating characteristic curves. Our findings pave the way for the development of practical microwave quantum illumination systems.
Quantum illumination leverages entanglement to surpass classical target detection, even in high-noise environments. Remarkably, its quantum advantage persists despite entanglement degradation caused by environmental decoherence. A central challenge lies in designing optimal receivers to exploit this advantage, with the correlation-to-displacement conversion module emerging as a promising candidate. However, the practical implementation of the conversion module faces technical hurdles, primarily due to the vast number of modes involved. In this work, we address these challenges by proposing a frequency-mode entangled source with matched photon numbers, a heterodyne detection scheme for the returned signals across vast modes, and a cavity-enhanced quantum pulse gate for programmable mode processing. This integrated framework paves the way for the realization of practical quantum illumination systems.
Quantum illumination leverages entanglement to surpass classical target detection, even in high-noise environments. Remarkably, its quantum advantage persists despite entanglement degradation caused by environmental decoherence. A central challenge lies in designing optimal receivers to exploit this advantage, with the correlation-to-displacement conversion module emerging as a promising candidate. However, the practical implementation of the conversion module faces technical hurdles, primarily due to the vast number of modes involved. In this work, we address these challenges by proposing a frequency-mode entangled source with matched photon numbers, a heterodyne detection scheme for the returned signals across vast modes, and a cavity-enhanced quantum pulse gate for programmable mode processing. This integrated framework paves the way for the realization of practical quantum illumination systems.
Quantum illumination leverages entanglement to surpass classical target detection, even in high-noise environments. Remarkably, its quantum advantage persists despite entanglement degradation caused by environmental decoherence. A central challenge lies in designing optimal receivers to exploit this advantage, with the correlation-to-displacement (C→D) conversion module emerging as a promising candidate. However, practical implementation remains technically demanding, particularly in realizing a low-noise programmable mode selector. In this work, we propose a scheme for the C→D module that incorporates a cavity-enhanced quantum pulse gate for programmable mode processing, achieving performance close to the theoretical optimum. This integrated framework paves the way for the realization of practical quantum illumination systems.