First-photon target detection: Beating Nair's pure-loss performance limit

In 2011, Nair published a no-go theorem for quantum radar target detection [Phys. Rev. A 84, 032312 (2011)]. He showed, under fairly general assumptions, that a coherent-state radar's error probability was within a factor of two of the best possible quantum performance for the pure-loss (no background radiation) channel whose roundtrip radar-to-target-to-radar transmissivity kappa satisfies kappa << 1. We introduce first-photon radars (FPRs) to circumvent and beat Nair's performance limit. FPRs transmit a periodic sequence of pulses, each containing NS photons on average, and perform ideal direct detection (photon counting at unit quantum efficiency and no dark counts) on the returned radiation from each transmission until at least one photon has been detected or a preset maximum of M pulses has been transmitted. They decide a target is present if and only if they detect one or more photons. We consider both quantum (each transmitted pulse is a number state) and classical (each transmitted pulse is a coherent state) FPRs, and we show that their error-probability exponents are nearly identical when kappa << 1. With the additional assumption that kappa N-S << 1, we find that their advantage in error-probability exponent over Nair's performance limit grows to 3 dB as M -> infinity. However, because FPRs' pulse-repetition period must exceed the radar-to-target-to-radar propagation delay, their use in standoff sensing of moving targets will likely employ kappa N-S similar to 1 and M similar to 10 and achieve similar to 2 dB advantage. Our work constitutes an FPR version of Nair's no-go theorem for quantum radar target detection.