Several quantum radar concepts have been proposed that exploit the entanglement found in two-mode squeezed vacuum states of the electromagnetic field, the most prominent being radar based on quantum illumination. Classical radars are sometimes required to distinguish between true echos of their transmitted signals and signals generated by interferors or spoofers. How vulnerable to spoofing is quantum illumination? We analyze the scenario of a radar operator trying to detect the presence of a classical spoofer employing a measure-and-prepare strategy against a quantum radar. We consider two spoofing strategies - (1) direct detection and number state preparation, and (2) heterodyne detection and coherent state preparation. In each case, the radar operator performs a hypothesis test to decide if received pulses are true returns or spoofs. Since the spoofer can not reproduce the entanglement with modes retained by the radar operator, both approaches to spoofing are to some extent detectable. We quantify the effectiveness of the spoof in terms of the fidelity between the real return and the spoof return, and the probability of error in spoof detection. We find that in the absence of noise and loss, direct detection tends to produce spoofs with greater fidelity, which are therefore harder to detect. Moreover, this advantage survives the introduction of noise and loss into the model. Our results suggest that entanglement is a novel resource available to quantum radar for detecting spoofing.
Several quantum radar concepts have been proposed that exploit the entanglement found in two-mode squeezed vacuum states of the electromagnetic field, the most prominent being radar based on quantum illumination. Classical radars are sometimes required to distinguish between true echos of their transmitted signals and signals generated by interferors or spoofers. How vulnerable to spoofing is quantum illumination? We analyze the scenario of a radar operator trying to detect the presence of a classical spoofer employing a measure-and-prepare strategy against a quantum radar. We consider two spoofing strategies - (1) direct detection and number state preparation, and (2) heterodyne detection and coherent state preparation. In each case, the radar operator performs a hypothesis test to decide if received pulses are true returns or spoofs. Since the spoofer can not reproduce the entanglement with modes retained by the radar operator, both approaches to spoofing are to some extent detectable. We quantify the effectiveness of the spoof in terms of the fidelity between the real return and the spoof return, and the probability of error in spoof detection. We find that in the absence of noise and loss, direct detection tends to produce spoofs with greater fidelity, which are therefore harder to detect. Moreover, this advantage survives the introduction of noise and loss into the model. Our results suggest that entanglement is a novel resource available to quantum radar for detecting spoofing.
Electromagnetic remote sensing technologies, such as radar and lidar, can be misled by targets that generate spoof pulses. Typically, spoofing a transmitted signal involves measuring its properties to prepare a spoof signal that is a close enough copy of the original to fool a receiver. Quantum physics imposes a hard limit on the information that can be gained by the spoofer through a measurement on the transmitted signal. Here we analyze an idealized spoofing scenario to consider broadly the limits to spoofing imposed by quantum resources. We show that a spoofer optimally employing classical information on the state of the transmitted signal (i.e., the best measure-and-prepare strategy allowed by quantum mechanics) inevitably emits imperfect spoofs that can be exploited by the receiver to reveal the presence of the spoofer, or to discriminate between true reflections and spoofs. We first analyze a sensor employing a transmitted signal chosen randomly from a set of nonorthogonal, coherent states. Quantum-noise-limited measurements by the spoofer cannot perfectly identify the signal transmitted, leading inevitably to detectable spoofing errors [1]. We show that heterodyne reception and thresholding closely approaches quantum optimal spoof detection performance for this type of signal [2]. We next consider a quantum illumination sensor, a technology that exploits entanglement to achieve a quantum advantage in target detection. We consider two spoofing strategies - (1) direct detection and number state preparation, and (2) heterodyne detection and coherent state preparation. In both cases, the spoofer’s measure-and-prepare strategy is unable to reproduce in a spoof signal the quantum entanglement between the transmitted signal and retained modes at the receiver, again leading to inevitable spoofing errors [3].
Electromagnetic remote sensing technologies such as radar can be misled by targets that generate spoof pulses. Typically, a would-be spoofer must make measurements to characterize a received pulse in order to design a convincing spoof pulse. The precision of such measurements is ultimately limited by quantum noise. Here we introduce a model of electromagnetic spoofing that includes effects of practical importance that were neglected in prior theoretical studies. In particular, the model includes thermal background noise and digital quantization noise, as well as loss in transmission, propagation, and reception. We derive the optimal probability of detecting a spoofer allowed by quantum physics. We show that heterodyne reception and thresholding closely approaches this optimal performance. Finally, we show that a high degree of certainty in spoof detection can be reached by Bayesian inference from a sequence of received pulses. Together these results suggest that a practically realizable receiver could plausibly detect a radar spoofer by observing errors in the spoof pulses due to quantum noise. Published by the American Physical Society 2024
Spoofing an electromagnetic signal involves measuring its properties and preparing a spoof signal that is a close enough copy to fool a receiver. A classic application of spoofing is in radar where an airborne target attempts to avoid being tracked by a ground-based radar by emitting pulses indicating a false range or velocity. In certain scenarios it has been shown that a sensor can exploit quantum mechanics to detect spoofing at the single-photon level. Here we analyze an idealized spoofing scenario where a transmitter-receiver pair, seeking to detect spoofing, utilizes a signal chosen randomly from a set of nonorthogonal, coherent states. We show that a spoofer optimally employing classical information on the state of the transmitted signal (i.e., the best measure-and-prepare strategy allowed by quantum mechanics) inevitably emits imperfect spoofs that can be exploited by the receiver to reveal the presence of the spoofer, or to discriminate between true reflections and spoofs. Importantly, we show that the quantum limitations on classical spoofing remain significant even in the large mean-photon-number regime.
There has been a great interest in quantum metrology (e.g., quantum interferometric radar) due to its applications in sub-Rayleigh ranging and remote sensing. Despite interferometric radar has received vast amount of attentions over the past two decades, very few researches has been conducted on another type of quantum radar: quantum illumination radar, or more precisely quantum target detection. It is, in general, used to interrogate whether the low-reflectivity target in a noisy thermal bath is existed using quantum light. The entanglement properties of its emitted light source give it a unique detection advantage over the classical radar. Entangled coherent state (ECS), as a class of quantum states with high entanglement robustness in noisy environments, has been widely used in several fields of quantum science such as quantum informatics, quantum metrology . In this paper, we investigate the target detection performance of quantum illumination radar based on three different types of ECS states. We employ the two-mode squeezed vacuum state (TMSV) and the coherent state as benchmarks to compare and analyze the relationship between the entanglement strength of the three types of ECS states and their quantum illumination detection performance. We found that the detection performance of the three ECS states is better than that of the coherent state. However, it is inferior to that of the TMSV state when the target is of low reflectivity. The emitted photon number is much smaller than the background noise (we call this as “good” illumination conditions). On the contrary, quantum illumination radar has no obvious advantage over coherent state radar for target detection under other illumination conditions; further, the detection performance of these three types of ECS states is not evidently related to that of the TMSV state and the coherent state. Finally, we reveal that the target detection performance of quantum illumination for the first two types of ECS states can be determined by their entanglement strength under “good” illumination conditions by adjusting the inter-modal phase of these two ECS states while keeping the emitted photon number constant. Under other illumination conditions, there is no evidence to demonstrate the entanglement strength of ECS states being associated with their target detection performance.
A Doppler radar is a device that employs the Doppler effect to estimate the radial velocity of a moving target at a distance. Traditional radars are based on a classical description of the electromagnetic radiation, but in principle their performance can be improved employing entangled quantum probe states. For target detection, i.e. hypothesis testing, a quantum advantage exists even in the high-noise regime appropriate to describe microwave fields, a protocol known as quantum illumination. In this paper, we show a similar advantage also for a quantum Doppler radar operating in presence of thermal noise, whereas so far a quantum advantage was shown in the noiseless scenario or in lidars operating at optical frequencies with negligible thermal noise. Concretely, we quantify the radar performance in terms of the quantum Fisher information, which captures the ultimate precision allowed by quantum mechanics in the asymptotic regime. We compare a classical protocol based on coherent states with a quantum one that uses multimode states obtained from spontaneous parametric downconversion. To ensure a fair comparison we match the signal energy and pulse duration. We show that a 3dB advantage is possible in the regime of small number of signal photons and high thermal noise, even for low transmissivity.
Abstract Quantum illumination has been proposed as a theoretical route to detecting low-reflectivity targets, such as stealth aircraft, in high-background-noise environments where classical radar performance degrades. The protocol, as originally formulated (Lloyd, 2008; Tan et al., 2008), uses continuous-variable entangled light (two-mode squeezed vacuum) and a specific phase-sensitive joint receiver to achieve a theoretical detection advantage over classical illumination of matched energy, even though the entanglement itself does not survive the round trip through a lossy, noisy channel. This study investigates whether that advantage appears in a simpler, discrete-variable (qubit) toy model, of the kind commonly used for pedagogical intuition, implemented on PKTron and cross-checked on IBM Quantum hardware. A rigorously fair comparison was constructed in which an entangled Bell pair and a classically correlated (separable) mixture of matched initial correlation strength were each subjected to identical loss and background-noise channels, with detection performance assessed via the same joint correlation measurement (Z⊗Z expectation) in both cases. In PKTron simulation, the entangled probe showed a correlation separation between target-present and target-absent hypotheses of 0.0100 at zero background noise, decreasing to 0.0025 at high background noise, while the classically correlated probe showed a substantially larger separation, decreasing from 0.1000 to 0.0500 over the same range — indicating no entanglement advantage, and if anything, a disadvantage, in this discrete model. This qualitative finding was independently corroborated on IBM Quantum's ibm_kingston hardware, using natural qubit T1 relaxation (rather than an artificially injected noise parameter) as the loss channel: entangled correlation degraded to 54.5% of its initial value after 60 microseconds, compared to 77.7% retained by the classically correlated mixture over the same interval. These results indicate that the theoretical quantum illumination advantage does not straightforwardly emerge from a simple discrete-qubit correlation model, consistent with the broader understanding that the effect is specific to continuous-variable Gaussian states and phase-sensitive joint detection, and consistent with quantum illumination's status as a theoretical concept with no demonstrated range or signal-to-noise advantage over classical radar to date.