  We present the full characterization of phase-randomized or phase-averaged
coherent states, a class of states exploited in communication channels and in
decoy state-based quantum key distribution protocols. In particular, we report
on the suitable formalism to analytically describe the main features of this
class of states and on their experimental investigation, that results in
agreement with theory. We also show the results we obtained by manipulating the
phase-averaged coherent states with linear optical elements and testify their
good quality by employing some non-Gaussianity measures and the concept of
mutual information.
