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IEEE Transactions on Radar Systems

Engineering Constraints and Application Regimes of Quantum Radar

Florian Bischeltsrieder, Michael Würth, Johannes A. Russer, Markus Peichl, Wolfgang Utschick

Published Jan 1, 2024• 6 citations
Publisher

Abstract

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.

DOI
10.1109/trs.2024.3361048

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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.
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.
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.
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 alternative to classical radar for target detection. Quantum radar systems utilize a quantum physics term known as quantum entanglement for target detection, which has higher correlation that cannot be achieved by classical sources. The results of the quantum radar analysis have shown that employing a pair of entangled sources has an advantage about a 6 dB in target detection compared to the classical counterpart. These analyses have also been tested experimentally in both optical and microwave frequency domains. These experimental setups have shown that this supremacy level might be achieved under ideal conditions, but it is not possible with the current experimental setups. Nevertheless, employment of quantum physics laws is a new field of study for engineering discipline, with the development of measurement instruments researchers might reach this superiority level.
At the current state of the scientific discourse on quantum radar, the best understood and experimentally feasible types of implementation are based on two-mode-squeezed-vacuum photon states and aimed at the task of target detection. The operating environment, in which an advantage over classical radar may be attainable, is thereby limited to the extreme regimes of very low signal-to-noise ratios and high thermal noise levels as well as confining the required hardware at mK temperatures. In this work, we approach the open question of how to optimally operate a potential quantum radar system. To this end, we define the optimal operation by means of the detection advantage against classical radar as well as the efficient usage of the resource measurement time. We show that there is a trade-off between time-efficiency and out-performance of classical radar and specify the conditions for such an operation. Building on this aspect, we investigate the concept of the fair classical comparison to facilitate the understanding of its relation to quantum radar.
We describe an experiment which comes very close to implementing a quantum radar based on entangled microwaves. A pair of entangled microwave beams are generated using a Josephson parametric amplifier (JPA) and measured by a pair of digitizers after amplification. We present a receiver operating characteristic (ROC) curve for the case where the signal power at the digitizers is −83.84 dBm (corresponding to a JPA power output, before amplification, of −148.26 dBm), as well as for a classically correlated source which attempts to approximate the covariance structure of the entangled JPA signals. The entangled signals are seen to be clearly superior to the classically correlated signals. Although the latter is still interesting from a noise radar perspective, this demonstrates that attempting to simulate entanglement with classical signals causes a measurable decrease in correlation. Our experiment validates the feasibility and desirability of a microwave quantum radar.