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

TL;DR

This paper introduces first-photon radars (FPRs) that outperform Nair's pure-loss quantum radar detection limit by using sequential photon detection, achieving a 2-3 dB advantage in error probability exponent under realistic conditions.

Contribution

The paper presents FPRs that beat Nair's no-go theorem for quantum radar detection by employing sequential photon detection strategies with both quantum and classical states.

Findings

FPRs nearly match quantum and classical error exponents for small transmissivity

Error-probability exponent advantage grows to 3 dB with many pulses under ideal conditions

Realistic scenarios with limited pulses still achieve about 2 dB advantage

Abstract

In 2011, Nair published a no-go theorem for quantum radar target detection [Phys. Rev. A {\bf 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 $\kappa \ll 1$. We introduce first-photon radars (FPRs) to circumvent and beat Nair's performance limit. FPRs transmit a periodic sequence of pulses, each containing $N_S$ 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 pre-set 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 $\kappa \ll 1$. With the additional assumption that $\kappa N_S \ll 1$, we find that their advantage in error-probability exponent over Nair's performance limit grows to 3 dB as $M \rightarrow \infty$. 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 $\kappa N_S \sim 1$ and $M \sim 10$ and achieve ~2 dB advantage. Our work constitutes a new no-go theorem for quantum radar target detection.