  We experimentally investigate the non-Gaussian features of the
phase-randomized coherent states, a class of states exploited in communication
channels and in decoy state-based quantum key distribution protocols. In
particular, we reconstruct their phase-insensitive Wigner functions and
quantify their non-Gaussianity. The measurements are performed in the
mesoscopic photon-number domain by means of a direct detection scheme involving
linear detectors.
