Photon Counting for a Number State Passing through a Laser Channel

We investigate the photon counting for a pure number state passing through a laser channel. It is found that the pure number state evolves in the laser channel into a mixed state: the number state |m??m| evolves into a superposition of the photon-added thermal (chaotic) state, and the photon counting for the outcome state is a Gauss hypergeometric function.