  We compare the performance of a quantum radar based on two-mode squeezed
states with a classical radar system based on correlated thermal noise. With a
constraint of equal number of photons $N_S$ transmitted to probe the
environment, we find that the quantum setup exhibits an advantage with respect
to its classical counterpart of $\sqrt{2}$ in the cross-mode correlations.
Amplification of the signal and the idler is considered at different stages of
the protocol, showing that no quantum advantage is achievable when a
large-enough gain is applied, even when quantum-limited amplifiers are
available. We also characterize the minimal type-II error probability decay,
given a constraint on the type-I error probability, and find that the optimal
decay rate of the type-II error probability in the quantum setup is
$\ln(1+1/N_S)$ larger than the optimal classical setup, in the $N_S\ll1$
regime. In addition, we consider the Receiver Operating Characteristic (ROC)
curves for the scenario when the idler and the received signal are measured
separately, showing that no quantum advantage is present in this case. Our work
characterizes the trade-off between quantum correlations and noise in quantum
radar systems.
