Quantum illumination for enhanced detection of Rayleigh-fading targets

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, Phys. Rev. Lett. 118, 040801 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.040801] - 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(MκNS/NB), when MκNS/NB1, with M1 being the QI transmitter's time-bandwidth product, NS1 its brightness, κ the target return's average intensity, and NB the background light's brightness.