Coherent-state phase concentration by quantum probabilistic amplification

We propose a probabilistic measurement-induced amplification for coherent states. The amplification scheme uses a counterintuitive architecture: a thermal noise addition (instead of a single-photon addition) followed by a feasible multiple-photon subtraction using a realistic photon-number-resolving detector. It allows one to substantially amplify weak coherent states and simultaneously reduce their phase uncertainty, which is impossible when using a deterministic Gaussian amplifier.