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.
Highlights
Introduction.—Classical microwave radars use time-offlight measurement to infer the range to a distant target from its return’s round-trip range delay τ [1,2,3,4,5,6,7]
Our proposed quantum illumination (QI) ranging is a quantum pulsecompression radar that benefits from the entanglement between a high time-bandwidth product transmitted signal pulse and a high time-bandwidth product retained idler pulse
To find the Ziv-Zakai bound (ZZB) for our quantum radar, we will focus on the NS ≪ 1; κ ≪ 1; NB ≫ 1 regime and use the quantum Chernoff bound (QCB) for range-bin discrimination that applies when T ≫ Δτ [27,33], as will be necessary for our quantum radar to reach its threshold signal-to-noise ratio (SNR), viz., Peðτ0Þ ≤ exp1⁄2−2SNRð1 − e−Δω2τ02=2Þ=2; ð19Þ
Summary
Introduction.—Classical microwave radars use time-offlight measurement to infer the range to a distant target from its return’s round-trip range delay τ [1,2,3,4,5,6,7]. Their ultimate range-delay measurement accuracy for a single target, i.e., the minimum root-mean-squared (rms) estimation error δτmin for localizing a single target, as set by the Cramer-Rao bound (CRB), decreases as the signal-to-noise ratio (SNR) increases. That first step toward understanding QI’s ranging performance did not address QI’s ultimate range-delay accuracy, as set by the quantum CRB [28,29,30] at high SNR and the quantum Ziv-Zakai bound (ZZB) [31] in the subthreshold SNR region.
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