  Quantum-limited amplifiers increase the amplitude of quantum signals at the
price of introducing additional noise. Quantum purification protocols operate
in the reverse way, by reducing the noise while attenuating the signal. Here we
investigate a scenario that interpolates between these two extremes. We search
for the optimal physical process that generates $M$ approximate copies of pure
and amplified coherent state, starting from $N$ copies of a noisy coherent
state with Gaussian modulation. We prove that the optimal deterministic
processes are always Gaussian, whereas non-Gaussianity powers up probabilistic
advantages in suitable parameter regimes. The optimal processes are
experimentally feasible, both in the deterministic and in the probabilistic
scenario. In view of this fact, we provide benchmarks that can be used to
certify the experimental demonstration of the quantum-enhanced amplification
and purification of coherent states.
