  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. We
derive that limit through continuous-time quantum analysis and show that
quantum illumination (QI) 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 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.
