High time-bandwidth product waveforms have long been used in radar systems to achieve high-resolution ranging at high signal-to-noise ratio under a peak power constraint on the radar transmitter. We consider a laser radar system in which a series of N-photon entangled-state pulses are prepared with only one photon from each pulse being used to interrogate the target while the others are detected within the radar itself. This send-one-detectall protocol (SODAP) achieves high time-bandwidth product pulse compression in a cryptographic quantum manner, i.e., the entanglement precludes any passive receiver from performing pulse compression on the target return.
High time-bandwidth product waveforms have long been used in radar systems to achieve high-resolution ranging at high signal-to-noise ratio under a peak power constraint on the radar transmitter. We consider a laser radar system in which a series of N-photon entangled-state pulses are prepared with only one photon from each pulse being used to interrogate the target while the others are detected within the radar itself. This send-one-detectall protocol (SODAP) achieves high time-bandwidth product pulse compression in a cryptographic quantum manner, i.e., the entanglement precludes any passive receiver from performing pulse compression on the target return.
Radars use time-of-flight measurement to infer the range to a distant target from its return's round-trip range delay. They typically transmit a high time-bandwidth product waveform and use pulse-compression reception to simultaneously achieve satisfactory range resolution and range accuracy under a peak transmitted-power constraint. Despite the many proposals for quantum radar, none have delineated the ultimate quantum limit on ranging accuracy. We derive that limit through continuous-time quantum analysis and show that quantum illumination ranging-a quantum pulse-compression radar that exploits the entanglement between a high time-bandwidth product transmitted signal pulse and and a high time-bandwidth product retained idler pulse-achieves that limit. We also show that quantum illumination ranging offers mean-squared range-delay accuracy that can be tens of dB better than that of a classical pulse-compression radar of the same pulse bandwidth and transmitted energy.
Abstract Entanglement has been known to boost target detection, despite it being destroyed by lossy-noisy propagation. Recently, Zhuang and Shapiro (2022 Phys. Rev. Lett. 128 010501) proposed a quantum pulse-compression radar to extend entanglement’s benefit to target range estimation. In a radar application, many other aspects of the target are of interest, including angle, velocity and cross section. In this study, we propose a dual-receiver radar scheme that employs a high time-bandwidth product microwave pulse entangled with a pre-shared reference signal available at the receiver, to investigate the direction of a distant object and show that the direction-resolving capability is significantly improved by entanglement, compared to its classical counterpart under the same parameter settings. We identify the applicable scenario of this quantum radar to be short-range and high-frequency, which enables entanglement’s benefit in a reasonable integration time.
This article presents a comprehensive analysis of two classes of quantum radars, including quantum direct-detection and quantum-entangled noise radars. In the first case, inspired by the well-established concept of single-photon LiDARs, we investigated the performance of single-photon radars, in which state-of-the-art single microwave-photon detectors are employed to enhance the detection sensitivity and enable the detection of weaker signals. We derived analytical expressions for the maximum detection range of both classes of quantum radars in terms of the Lambert W function, by considering all relevant system, target, and environmental parameters. Our formulation facilitates direct comparison of noise radars with direct-detection radars and suggests that a quantum-entangled noise radar can be regarded as an enhanced direct-detection radar with an effective threshold signal-to-noise ratio. Furthermore, we applied this framework to classical-correlated noise radars and defined the parameter range enhancement factor (REF) to quantify the superiority of quantum-entangled noise radars over their classical counterparts. Moreover, we introduced a rule-of-thumb for approximating the REF. We also examined the influence of limitations imposed by various microwave detection technologies. Our analysis shows that the conventional antennas limit the potential benefits of quantum-entangled noise radar systems. We also demonstrated that the optimal detection method for these radars is a microwave detector based on a quantum transducer combined with a single optical-photon detector. We showed that, with the current technology, implementing a quantum-entangled noise radar with the maximum detection range on the order of few kilometers is possible. Finally, we explored the potential applications of quantum-entangled noise radars.
Quantum radar is an emerging technique, currently at the experimental stage, that promises to disrupt the well-established field of conventional radar. Recent progress shows that it is possible to generate and use entangled pairs of microwave photons for detection purposes and to obtain an advantage over a classical radar. In this work, we study the currently experimentally feasible type of quantum correlation radar. To this end, we compare different radar architectures, quantum and classical, by analyzing their detection performances by means of the receiver operating characteristic (ROC), the minimum error probability as well as the Chernoff bound. The underlying system models are based on quantum mechanical formulations as well as conventional signal theory. Where it is appropriate and necessary to facilitate our analysis, we apply the central limit theorem to establish the Gaussianity of the observable quantities. A conceptual analogy between the quantum and classic points-of-view is drawn and supported by results showing the asymptotic behavior of the ROC curves of both physical descriptions depending on the power levels of signal and noise. We come to exact and comprehensible conclusions on the current state of quantum radar in comparison to classic radar with a detailed mapping of the radar operating regime (measurement time, signal-to-noise ratio, environmental noise level, target object size and distance) in which a quantum advantage is attainable.
Quantum radars and lidars are a novel, much-discussed, and rapidly evolving field of quantum science and technology, promising remarkable advantages in such basic tasks as target detection, ranging, and recognition. Quantum radars and lidars have already moved from the realm of theoretical considerations toward experiments, green, and as is the case for lidars, toward practical applications. Here we review the underlying concepts and present the basic configurations of quantum radars and lidars based on photonic entanglement and single-photon detection. We also briefly discuss the methods of producing entangled photons, such as spontaneous parametric down conversion (SPDC), spontaneous four-wave mixing, Josephson parametric amplifiers (JPAs), and quantum antennas. We show that quantum technologies open promising avenues toward the enhancement of signal-to-noise ratio (SNR) and overcoming the Rayleigh limit in radar and lidar systems.
Quantum radar (QR) has been shown to provide enhanced performance in target detection and parameter estimation, while its resolution capability remains largely unexplored. In classical radar theory, the ambiguity function is used to characterize waveform resolution capability. However, the volume invariance of the ambiguity function and the uncertainty relation of the Fourier transform impose fundamental limitations on the resolution capability of any single waveform. In this paper, we extend the idea of waveform ambiguity function to QR systems, thereby developing a quantum ambiguity function (QAF) that enables the evaluation of the ultimate resolution of quantum states and serves as a guide for quantum state design. We show that quantum entanglement reduces the volume of the QAF and increases the time- bandwidth product, thereby overcoming these classical limitations. Furthermore, by drawing an analogy to classical waveform modulation, we show how modulating entangled states can further improve resolutions and elucidate the underlying mechanisms of these improvements.