  Gaussian quantum states hold special importance in the continuous variable
(CV) regime. In quantum information science, the understanding and
characterization of central resources such as entanglement may strongly rely on
the knowledge of the Gaussian or non-Gaussian character of the quantum state.
However, the quantum measurement associated with the spectral photocurrent of
light modes consists of a mixture of quadrature observables. Within the
framework of two recent papers [Phys. Rev. A 88, 052113 (2013) and Phys. Rev.
Lett. 111, 200402 (2013)], we address here how the statistics of the spectral
photocurrent relates to the character of the Wigner function describing those
modes. We show that a Gaussian state can be misidentified as non-Gaussian and
vice-versa, a conclusion that forces the adoption of tacit \textit{a priori}
assumptions to perform quantum state reconstruction. We experimentally analyze
the light beams generated by the optical parametric oscillator (OPO) operating
above threshold to show that the data strongly supports the generation of
Gaussian states of the field, validating the use of necessary and sufficient
criteria to characterize entanglement in this system.
