Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2307.02656 · Physical Review Research

Revealing spoofing of classical radar using quantum noise

Jonathan N. Blakely, Shawn D. Pethel, Kurt A. Jacobs

Published Feb 20, 2024• 2 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/physrevresearch.6.013179

Related papers

Quantum Resources for Detecting Spoofing of an Electromagnetic Signal

Jonathan N. Blakely, Shawn D. Pethel, Kurt A. Jacobs

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].

IEEE Conference on Antenna Measurements and Applications (CAMA)•Nov 18, 2025•0 citations

Quantum limits to classically spoofing an electromagnetic signal

Jonathan N. Blakely, Shawn D. Pethel

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.

arXiv:2201.09999•Physical Review Research•Jun 2, 2022•7 citations

Revealing spoofing of quantum illumination using entanglement

Jonathan N. Blakely, Shawn D. Pethel, Kenneth R. Stewart +1 more

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.

arXiv:2410.08353•Oct 10, 2024•0 citations

Quantum enhancement of spoofing detection with squeezed states of light

Tomás P. Espinoza, Sebastian Camilo Carrasco, Jose Antonio Rogan +2 more

We employ quantum state discrimination theory to establish the ultimate limit for spoofing detection in electromagnetic signals encoded with random quantum states. Our analysis yields an analytical expression for the optimal bound, which we prove can be achieved using a pair of coherent states. Notably, the quantum enhancement persists regardless of photon number, thereby removing the previous constraint to single-photon sources. This breakthrough unlocks new experimental possibilities using standard laser sources. Furthermore, we explore the encoding of squeezed states and demonstrate that the detection probability approaches 100% when the spoofer's capability is restricted to coherent-state generation. Published by the American Physical Society 2024

arXiv:2406.14750•Physical Review Research•Nov 27, 2024•2 citations

Bounds on Probability of Detection Error in Quantum-Enhanced Noise Radar

Jonathan N. Blakely

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.

Quantum Reports•Jul 21, 2020•7 citations

Engineering Constraints and Application Regimes of Quantum Radar

Florian Bischeltsrieder, Michael Würth, Johannes A. Russer +2 more

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.

IEEE Transactions on Radar Systems•Jan 1, 2024•6 citations
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
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].
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.
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.
We employ quantum state discrimination theory to establish the ultimate limit for spoofing detection in electromagnetic signals encoded with random quantum states. Our analysis yields an analytical expression for the optimal bound, which we prove can be achieved using a pair of coherent states. Notably, the quantum enhancement persists regardless of photon number, thereby removing the previous constraint to single-photon sources. This breakthrough unlocks new experimental possibilities using standard laser sources. Furthermore, we explore the encoding of squeezed states and demonstrate that the detection probability approaches 100% when the spoofer's capability is restricted to coherent-state generation. Published by the American Physical Society 2024
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.
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.