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arXiv:2311.14546 · Physical Review Letters

Heisenberg-Limited Quantum Lidar for Joint Range and Velocity Estimation

Maximilian Reichert, Quntao Zhuang, Mikel Sanz

Published Sep 26, 2024• 15 citations
arXivHTMLPDF

Abstract

We propose a quantum lidar protocol to jointly estimate the range and velocity of a target by illuminating it with a single beam of pulsed displaced squeezed light. In the lossless scenario, we show that the mean-squared errors of both range and velocity estimations are inversely proportional to the squared number of signal photons, simultaneously attaining the Heisenberg limit. This is achieved by engineering the multiphoton squeezed state of the temporal modes and adopting standard homodyne detection. To assess the robustness of the quantum protocol, we incorporate photon losses and detuning of the homodyne receiver. Our findings reveal a quantum advantage over the best-known classical strategy across a wide range of round-trip transmissivities. Particularly, the quantum advantage is substantial for sufficiently small losses, even when compared to the optimal-potentially unattainable-classical performance limit. The quantum advantage also extends to the practical case where quantum engineering is done on top of a strong classical coherent state with watts of power. This, together with the robustness against losses and the feasibility of the measurement with state-of-the-art technology, make the protocol highly promising for near-term implementation.

DOI
10.1103/physrevlett.133.130801

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We propose a quantum lidar protocol to jointly estimate the range and velocity of a target by illuminating it with a single beam of pulsed displaced squeezed light. In the lossless scenario, we show that the mean-squared errors of both range and velocity estimations are inversely proportional to the squared number of signal photons, simultaneously attaining the Heisenberg limit. This is achieved by engineering the multiphoton squeezed state of the temporal modes and adopting standard homodyne detection. To assess the robustness of the quantum protocol, we incorporate photon losses and detuning of the homodyne receiver. Our findings reveal a quantum advantage over the best-known classical strategy across a wide range of round-trip transmissivities. Particularly, the quantum advantage is substantial for sufficiently small losses, even when compared to the optimal-potentially unattainable-classical performance limit. The quantum advantage also extends to the practical case where quantum engineering is done on top of a strong classical coherent state with watts of power. This, together with the robustness against losses and the feasibility of the measurement with state-of-the-art technology, make the protocol highly promising for near-term implementation.
Abstract We propose a quantum-enhanced lidar system to estimate a target’s radial velocity, which employs squeezed and frequency-entangled signal and idler beams. We compare its performance against a classical protocol using a coherent state with the same pulse duration and energy, showing that quantum resources provide a precision enhancement in the estimation of the velocity of the object. We identify three distinct parameter regimes characterized by the amount of squeezing and frequency entanglement. In two of them, a quantum advantage exceeding the standard quantum limit is achieved assuming no photon losses. Additionally, we show that an optimal measurement to attain these results in the lossless case is frequency-resolved photon counting. Finally, we consider the effect of photon losses for the high-squeezing regime, which leads to a constant factor quantum advantage higher than 3 dB in the variance of the estimator, given a roundtrip lidar-to-target-to-lidar transmissivity larger than 50%.
Quantum light promises improved precision in optical remote sensing, but its practical advantage depends critically on whether nonclassical resources remain useful under realistic noise and experimentally accessible detection. This question becomes especially relevant for LiDAR systems, where a quantum advantage has been demonstrated for target detection and joint range-velocity estimation, but mostly under idealized conditions or simple noise models, such as optical loss and thermal background. A key open point is whether entanglement provides an operational advantage when the dominant disturbance is not independent noise, but structured interference across sensing modes. Here, we address this question by studying the joint estimation of target range and velocity with bright two-mode Gaussian probes and homodyne detection, comparing coherent, separable squeezed, and twin-beam states at a fixed resource budget. Our results reveal a hierarchy of quantum resources set by the noise structure: separable squeezing provides a robust advantage over coherent illumination under loss and thermal background, whereas twin-beam probes become superior under correlated jamming when the receiver is adaptively optimized. These results establish correlated noise as the operational regime in which entanglement provides a robustness advantage beyond local squeezing, opening a receiver-aware route to quantum-enhanced LiDAR in realistic and potentially adversarial environments.
Lidar is a well-known optical technology for measuring a target's range and radial velocity. We describe two lidar systems that use entanglement between transmitted signals and retained idlers to obtain significant quantum enhancements in simultaneous measurements of these parameters. The first entanglement-enhanced lidar circumvents the Arthurs-Kelly uncertainty relation for simultaneous measurements of range and radial velocity from the detection of a single photon returned from the target. This performance presumes there is no extraneous (background) light, but is robust to the round-trip loss incurred by the signal photons. The second entanglement-enhanced lidar---which requires a lossless, noiseless environment---realizes Heisenberg-limited accuracies for both its range and radial-velocity measurements, i.e., their root-mean-square estimation errors are both proportional to 1/M1/M1/M when MMM signal photons are transmitted. These two lidars derive their entanglement-based enhancements from the use of a unitary transformation that takes a signal-idler photon pair with frequencies ${\ensuremath{\omega}}_{S}$ and ${\ensuremath{\omega}}_{I}$ and converts it to a signal-idler photon pair whose frequencies are $({\ensuremath{\omega}}_{S}+{\ensuremath{\omega}}_{I})/2$ and $({\ensuremath{\omega}}_{S}\ensuremath{-}{\ensuremath{\omega}}_{I})/2$. Insight into how this transformation provides its benefits is provided through an analogy to continuous-variable superdense coding.
Quantum target ranging, which estimates a target position using entangled photon pairs, is known to offer an error-probability advantage over classical ranging strategies. Yet, realizing this advantage in practice remains challenging, as an existing receiver design relies on collective measurements and requires an impractically large number of quantum memories and linear passive components. In this work, we propose the hetero-homodyne receiver, a practically implementable architecture that achieves quantum advantage in target ranging using only local measurements. The receiver requires only one heterodyne setup, a single homodyne setup, and a delay line, making the implementation scalable and experimentally feasible. Our results establish a realistic framework for demonstrating quantum advantage in target ranging and contribute toward practical quantum radar systems.
Light Detection and Ranging (LiDAR) has emerged as a pivotal sensor across diverse domains such as autonomous driving, mapping, and remote sensing, owing to its exceptional orientation capabilities and high resolution. The detection mechanism of LiDAR is fundamentally categorized into non-coherent detection and coherent detection. Non-coherent detection employs the direct detection method, which involves measuring changes in the intensity of the reflected light signal to achieve detection. Pulse LiDAR, which determines the target range through pulsed time-of-flight measurements, falls within this classification. On the other hand, coherent detection employs heterodyne detection techniques and achieves detection by measuring the frequency or phase difference between the echo signal and the local oscillator signal. This approach is utilized in frequency modulation continuous wave (FMCW) LiDAR and Doppler speed LiDAR. LiDAR systems employing coherent detection methods can attain heightened sensitivity while operating at lower transmission power levels. However, due to the limitations posed by quantum noise, conventional LiDAR systems have encountered challenges in terms of detection sensitivity and resolution, prompting the need for advancement. In recent times, spurred by the emergence of quantum metrology, a quantum version of LiDAR has been conceptualized, promising superior precision and resolution. Leveraging the enhanced signal-to-noise ratio made possible by quantum advancements, quantum LiDAR demonstrates the potential to extend detection ranges, elevate detection accuracy, bolster anti-jamming capabilities, and enhance anti-stealth performance beyond that of classical LiDAR, all while operating at equivalent transmission signal power levels. As an emerging technology, quantum LiDAR is currently in its exploratory phase, and several challenges must be confronted prior to its practical implementation. These challenges encompass a restricted array of methods for the effective generation of quantum light sources, the vulnerability of quantum states to environmental factors, resulting in their deterioration, the constrained techniques for modulating quantum light sources, and the critical necessity to augment detector sensitivity. Furthermore, present quantum LiDAR efforts primarily concentrate on imaging and ranging capabilities, with limited research dedicated to simultaneous velocity measurement and ranging. Hence, forthcoming investigations into quantum LiDAR will center around optimizing quantum light source efficiency, exploring high-dimensional modulation techniques, and advancing high-sensitivity detectors. These efforts aim to enhance system stability and enable miniaturization, ultimately leading to superior target detection performance. This review centers on the evaluation of ranging and velocity measurement performance within quantum LiDAR systems. Following a concise introduction to two renowned categories of classical LiDAR—namely, pulse LiDAR and FMCW LiDAR, the paper delves into the progress made in quantum pulsed LiDAR and quantum interferometric LiDAR. In particular, this review highlights the advancements in quantum FMCW LiDAR, a system proposed for achieving simultaneous range and velocity measurements with quantum enhancement. By conducting a thorough assessment of the current accomplishments in quantum LiDAR research, the study seeks to attain a more profound comprehension of prevailing research focal points and obstacles, thus offering invaluable insights to steer its prospective advancement.