Ultimate limit of quantum pulse-compression ranging: hypothesis testing and parameter estimation

It is well known that entanglement can benefit quantum information processing tasks. Quantum illumination (QI), when first proposed, was surprising as the entanglement’s benefit survived entanglement-breaking noise. Since then, many efforts have been devoted to quantum sensing in noisy scenarios.  Such schemes, however, have been limited to binary quantum hypothesis testing for target detection, while classical radars are capable of more advanced sensing tasks.  For example, radars use time-of-flight measurement to infer the range to a distant target from its return's roundtrip 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.

 

First, we remove the binary-hypothesis limitation of QI by proposing a QI ranging protocol.  By formulating ranging as multiple-hypothesis testing, we show that entanglement affords a 6-dB advantage in error-probability exponent against the optimal classical scheme for localizing a target within a set of contiguous range-resolution bins.  Next, we take a parameter estimation approach and derive the range-delay accuracy limit through continuous-time quantum analysis.  We show that the QI ranging protocol — a quantum pulse-compression radar that exploits the entanglement between a high time-bandwidth product transmitted signal pulse and a high time-bandwidth product retained idler pulse — achieves that limit.  We also show that QI ranging offers mean-squared range-delay accuracy that can be 10's of dB better than a classical pulse-compression radar's of the same pulse bandwidth and transmitted energy.