  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.
