  We present the experimental investigation of the non-Gaussian nature of some
mixtures of Fock states by reconstructing their Wigner function and exploiting
two recently introduced measures of non-Gaussianity. In particular, we
demonstrate the consistency between the different approaches and the
monotonicity of the two measures for states belonging to the class of phase
randomized coherent states. Moreover, we prove that the exact behavior of one
measure with respect to the other depends on the states under investigation and
devise possible criteria to discriminate which measure is more useful for the
characterization of the states in realistic applications.
