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arXiv:2406.14750 · Physical Review Research

Quantum enhancement of spoofing detection with squeezed states of light

Tomás P. Espinoza, Sebastian Camilo Carrasco, Jose Antonio Rogan, J. A. Valdivia, Vladimir S. Malinovsky

Published Nov 27, 2024• 2 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/physrevresearch.6.043214

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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
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.
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].
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.
This thesis presents three studies in quantum-enhanced sensing and target detection. The first study explores covert target detection using optical or microwave probes, establishing quantum-mechanical limits on the error probabilities of entanglement-assisted detection methods while maintaining the sender's covertness. It identifies the minimal energy required to preserve covertness and reduce error probabilities, compares two-mode squeezed vacuum probes and coherent states against these limits, and extends the analysis to discriminating thermal loss channels and non-adversarial quantum illumination. The second study focuses on phase-insensitive optical amplifiers, determining the quantum limit on the precision of gain estimation using multimode probes possibly entangled with ancillary systems. It finds that the average photon number and the number of input modes are interchangeable resources for achieving optimal gain sensing precision, contrasting classical probes with quantum probes and highlighting the advantages of the latter, even with single-photon inputs and inefficient photodetection. It also provides a closed-form expression for the energy-constrained Bures distance between two amplifier channels. The third study compares three probe states -- coherent state, two-mode squeezed vacuum (TMSV), and single-photon entangled state (SPES) -- in quantum-enhanced target detection, assessing their performance under signal energy constraints relevant to covert radar sensing. SPES is uniquely positioned as a practical probe due to its non-classical properties after thermal loss and ease of generation. Numerical analysis shows that at low signal energies, the error exponent of TMSV aligns with SPES, indicating comparable detection capabilities and that SPES surpasses the best classical state-the coherent state-in accuracy for certain signal strengths.
Recently a number of laboratories have demonstrated the generation of squeezed light, a new kind of light which in some of its aspects exhibits less quantum noise then coherent light. Here a description will be given of how such light is generated and detected. With the successful generation and detection of squeezed light by a number of laboratories1-5 a new degree of control over the quantum statistics of light has been achieved. Light can now be generated which, in some of its aspects, has less quantum noise than coherent light. Such light may find applications in optical communications and in sensitive and precision measurement. Here a description will be given of how squeezed light is generated and detected.6-8 The discussion will be restricted to what is called "quadrature squeezing". The electric field operator for a single mode of the electromagnetic field can be written in the form