A two-step MaxLik-MaxEnt strategy to infer photon distribution from on/off measurement at low quantum efficiency

A method based on Maximum-Entropy (ME) principle to infer photon distribution from on/off measurements performed with few and low values of quantum efficiency is addressed. The method consists of two steps: at first some moments of the photon distribution are retrieved from on/off statistics using Maximum-Likelihood estimation, then ME principle is applied to infer the quantum state and, in turn, the photon distribution. Results from simulated experiments on coherent and number states are presented.