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 $1/M$ when $M$ 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.
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/M when M 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 \ensuremathωS and \ensuremathωI and converts it to a signal-idler photon pair whose frequencies are (\ensuremathωS+\ensuremathωI)/2 and (\ensuremathωS\ensuremath−\ensuremathωI)/2. Insight into how this transformation provides its benefits is provided through an analogy to continuous-variable superdense coding.
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%.
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.
The energy-time uncertainty relation puts a fundamental limit on the precision of lidars for the estimation of range and velocity. The precision in the estimation of the range (through the time of arrival) and the velocity (through Doppler frequency shifts) of a target are inversely related to each other and are dictated by the bandwidth of the signal. Here, we use the theoretical toolbox of multiparameter quantum metrology to determine the ultimate precision of the simultaneous estimation of range and velocity. We consider the case of a single target as well as a pair of closely separated targets. In the latter case, we focus on the relative position and velocity. We show that the tradeoff between the estimation precision of position and velocity is relaxed for entangled probe states and is completely lifted in the limit of perfect photon time-frequency correlations. In the regime where the two targets are close to each other, the relative position and velocity can be estimated nearly optimally and jointly, even without entanglement, using the measurements determined by the symmetric logarithmic derivatives.
The range and velocity of a moving object can be ascertained using the sensing technique known as light detection and ranging (lidar). It has recently been suggested that quantum lidar, which uses entangled states of light, can enhance the capabilities of lidar. Entangled pulsed light is used in prior quantum lidar approaches to assess both range and velocity at the same time using the time of flight and Doppler shift. However, the detection of entangled pulsed light is often inefficient and constrained by the temporal resolution of the detectors. Here, we investigate a quantum lidar utilizing a linear interferometer operating on a frequency-modulated continuous wave (FMCW) instead of pulses. Our findings demonstrate that the quantum FMCW lidar enables simultaneous measurements of range and velocity with quantum-enhanced accuracy and resolution, as well as superresolution phase imaging. Through self-heterodyne detection with a linear optical design, the signals of the quantum FMCW lidar with entangled photon pair can be efficiently carried out electronically by down-converting the optical signal to the microwave region. As a result, it is better suited for practical implementations.
Quantum light detection and ranging (LiDAR) utilizes quantum entanglement and correlation to improve precision, noise resilience and covertness of target detection. Despite recent advances, the development of a quantum LiDAR system that simultaneously achieves high precision and a large measurement range remains challenging. Here, we demonstrate a quantum amplitude-modulated continuous wave LiDAR with micrometer precision achievable via increased acquisition time and meter-scale measurement range. In our demonstration, the signal photons directly illuminate the target, while the idler photons are non-locally modulated with a high-frequency cosine wave and never interact with the target. By leveraging the non-local modulation and the quantum correlation, the target detection is achieved with a precision of 0.64 ± 0.06 mm within one second over a measurement range of 2-8 m. As the acquisition time is up to 500 s, the system achieves a precision of 29 ±4μm. Furthermore, our system realizes a 50 times precision improvement over the classical single-photon scheme in a background noise 37 dB stronger than the returned probe photons. With these advantages, our method will open venues for the development of high-precision, long-range, and noise-resilient target detection.
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.