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arXiv:2109.11079 · Physical Review Letters

Ultimate Accuracy Limit of Quantum Pulse-Compression Ranging

Quntao Zhuang, Jeffrey H. Shapiro

Published Jan 5, 2022• 60 citations
arXivHTMLPDF

Abstract

Radars use time-of-flight measurement to infer the range to a distant target from its return's round-trip range delay. They typically transmit a high time-bandwidth product waveform and use pulse-compression reception to simultaneously achieve satisfactory range resolution and range accuracy under a peak transmitted-power constraint. Despite the many proposals for quantum radar, none have delineated the ultimate quantum limit on ranging accuracy. We derive that limit through continuous-time quantum analysis and show that quantum illumination ranging-a quantum pulse-compression radar that exploits the entanglement between a high time-bandwidth product transmitted signal pulse and and a high time-bandwidth product retained idler pulse-achieves that limit. We also show that quantum illumination ranging offers mean-squared range-delay accuracy that can be tens of dB better than that of a classical pulse-compression radar of the same pulse bandwidth and transmitted energy.

DOI
10.1103/physrevlett.128.010501

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Radars use time-of-flight measurement to infer the range to a distant target from its return's round-trip range delay. They typically transmit a high time-bandwidth product waveform and use pulse-compression reception to simultaneously achieve satisfactory range resolution and range accuracy under a peak transmitted-power constraint. Despite the many proposals for quantum radar, none have delineated the ultimate quantum limit on ranging accuracy. We derive that limit through continuous-time quantum analysis and show that quantum illumination ranging-a quantum pulse-compression radar that exploits the entanglement between a high time-bandwidth product transmitted signal pulse and and a high time-bandwidth product retained idler pulse-achieves that limit. We also show that quantum illumination ranging offers mean-squared range-delay accuracy that can be tens of dB better than that of a classical pulse-compression radar of the same pulse bandwidth and transmitted energy.
High time-bandwidth product waveforms have long been used in radar systems to achieve high-resolution ranging at high signal-to-noise ratio under a peak power constraint on the radar transmitter. We consider a laser radar system in which a series of N-photon entangled-state pulses are prepared with only one photon from each pulse being used to interrogate the target while the others are detected within the radar itself. This send-one-detectall protocol (SODAP) achieves high time-bandwidth product pulse compression in a cryptographic quantum manner, i.e., the entanglement precludes any passive receiver from performing pulse compression on the target return.
Abstract Entanglement has been known to boost target detection, despite it being destroyed by lossy-noisy propagation. Recently, Zhuang and Shapiro (2022 Phys. Rev. Lett. 128 010501) proposed a quantum pulse-compression radar to extend entanglement’s benefit to target range estimation. In a radar application, many other aspects of the target are of interest, including angle, velocity and cross section. In this study, we propose a dual-receiver radar scheme that employs a high time-bandwidth product microwave pulse entangled with a pre-shared reference signal available at the receiver, to investigate the direction of a distant object and show that the direction-resolving capability is significantly improved by entanglement, compared to its classical counterpart under the same parameter settings. We identify the applicable scenario of this quantum radar to be short-range and high-frequency, which enables entanglement’s benefit in a reasonable integration time.
A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. This paper shows that quantum entanglement and squeezing can be employed to overcome the classical power/bandwidth limits on these procedures, enhancing their accuracy by a factor of the square root of the number of pulses employed times the number of photons per pulse. Frequency entangled pulses could be used to construct quantum positioning systems (QPS), to perform clock synchronization, or to do ranging (quantum radar): all of these techniques exhibit a similar enhancement compared with analogous protocols that use classical light.
It has been discussed recently how quantum illumination can be used to increase the accuracy of the value range-delay measurement \cite{Zhuang Shapiro 2022} in the domain of SNR compatible with current radar systems. However, the advantage described in [1] requires of a large integration time. In this work it is argued that multiple entangled photon quantum illumination could help to reduce the integration time when evaluating range-delay. Our analysis is performed in the framework of three entangled photon states discrete quantum illumination protocols. In this setting it is shown explicitly that using a direct generalization of Lloyd's protocol to the case where signal states describe two photons presents interesting advantages: 1. The reduction of the probability of error with respect to Lloyd's quantum illumination, 2. The reduction of the integration time with respect to Lloyd's quantum illumination, 3. The increase in the ultimate in the measurement of the range-delay accuracy.
Superposition and entanglement, the quintessential characteristics of quantum physics, have been shown to provide communication, computation, and sensing capabilities that go beyond what classical physics will permit. It is natural, therefore, to explore their application to radar, despite the fact that decoherence-caused by the loss and noise encountered in radar sensing-destroys these fragile quantum properties. This paper tells the story of “quantum illumination”, an entanglement-based approach to quantum radar, from its inception to its current understanding. Remarkably, despite loss and noise that destroys its initial entanglement, quantum illumination does offer a target-detection performance improvement over a classical radar of the same transmitted energy. A realistic assessment of that improvement's utility, however, shows that its value is severely limited. Nevertheless, the fact that entanglement can be of value on an entanglement-breaking channel-the meta-lesson of the quantum illumination story-should spur continued research on quantum radar.