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Optics Express

Comparison of SNR gain between quantum illumination radar and classical radar

Rongyu Wei, Jun Li, Weihao Wang, Songhao Meng, Baoshan Zhang, Qinghua Guo

Published Sep 12, 2022• 7 citations
Publisher

Abstract

It has been proved that quantum illumination (QI) radar has the quantum advantages in error-probability exponent. However, the error-probability exponent is not a recognized figure of merit in the radar literature, nor does it correspond in a straightforward manner to any such figure of merit. Signal to noise ratio (SNR) gain is an important criterion in radar theory. While, the theoretical analysis of quantum enhancement in SNR gain of QI radar has not been reported. In this paper, we compare the physical fundamental of matched filter (MF), which can achieve the optimal SNR gain under white noise in classical radar theory, and phase conjugation (PC) receiver. Furthermore, the quantum enhancement of SNR gain in QI radar is studied. It is shown that QI radar with practical receivers can achieve about 3dB quantum advantage in SNR gain. In addition, in the case of extremely weak signal, it can potentially achieve tens of dB enhancement in SNR gain compared with the MF based classical radar.

DOI
10.1364/oe.468158

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It has been proved that quantum illumination (QI) radar has the quantum advantages in error-probability exponent. However, the error-probability exponent is not a recognized figure of merit in the radar literature, nor does it correspond in a straightforward manner to any such figure of merit. Signal to noise ratio (SNR) gain is an important criterion in radar theory. While, the theoretical analysis of quantum enhancement in SNR gain of QI radar has not been reported. In this paper, we compare the physical fundamental of matched filter (MF), which can achieve the optimal SNR gain under white noise in classical radar theory, and phase conjugation (PC) receiver. Furthermore, the quantum enhancement of SNR gain in QI radar is studied. It is shown that QI radar with practical receivers can achieve about 3dB quantum advantage in SNR gain. In addition, in the case of extremely weak signal, it can potentially achieve tens of dB enhancement in SNR gain compared with the MF based classical radar.
Based on Quantum illumination (QI) protocol, researcshers have developed prototypes of quantum radar and demonstrated its quantum enhancement. Nevertheless, there are still difficulties in the practical application for QI radar, especially the trade-off between the detection range and quantum enhancement, as well as the construction of the optimized receiver. Some studies have suggested that the potential solutions to these difficulties are to deploy the quantum limited amplifiers in QI radars, and have envisioned different amplification schemes. In this paper, we establish a universal and effective method to evaluate the signal-to-noise ratio of QI radar. It connects QI radar theory with classical radar signal processing theory, providing support for researchers to evaluate the performance of various QI radar schemes from a radar perspective. Based on this method, we prove that any quantum limited phase-insensitive amplification scheme will seriously weaken the quantum enhancement of QI radar. Furthermore, we also demonstrate that the QI radar with phase-sensitive amplified idler has no advantage over the optimal classical illumination. These results can help us avoid some unreasonable QI radar schemes. In addition, we believe that the proposed method can also be applied to explore other potential QI radar schemes and contribute to promoting the application development of QI radar.
Abstract Based on quantum illumination (QI) protocol, microwave quantum radar has been developed, which has attracted great interest from radar researchers. While, according to the QI protocol, the quantum advantage of QI radar is related to the power of generated signal, which may lead to a trade‐off between its quantum advantage and the maximum detection range. However, the maximum detection range is an important indicator to measure the performance of the radar. Therefore, it is necessary to quantitatively analyse the maximum detection range and quantum advantages of microwave QI radar, which will help us understand its performance from the perspective of radar applications and further evaluate the potential application scenarios and future research directions of it. The microwave quantum radar equation is developed, by the authors, based on the classical radar equation with the consideration of the quantum properties of extremely weak signals. Then, the maximum detection range of QI radar and classical two mode noise radar in different microwave bands is comprehensively compared and analysed. The possible applications of microwave QI radars in different bands are also discussed. In addition, the authors demonstrate that the symmetrical quantum limited amplification actually has no contribution to improving the detection range of a QI radar.
We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons NStransmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of √2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/NS) larger than the optimal classical setup, in the NS<; <; 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.
We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons N-S transmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of root 2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/N-S) larger than the optimal classical setup, in the N-S << 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.
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.
Several methods for exploiting quantum effects in radar have been proposed, and some have been shown theoretically to outperform any classical radar scheme. Here, a model is presented of quantum-enhanced noise radar enabling a similar analysis. This quantum radar scheme has a potential advantage in terms of ease of implementation insofar as it requires no quantum memory. A significant feature of the model introduced is the inclusion of quantum noise consistent with the Heisenberg uncertainty principle applied to simultaneous determination of field quadratures. The model enables direct comparison to other quantum and classical radar schemes. A bound on the probability of an error in target detection is shown to match that of the optimal classical-state scheme. The detection error is found to be typically higher than for ideal quantum illumination, but orders of magnitude lower than for the most similar classical noise radar scheme.