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Gaussian quantum states hold special importance in the continuous variable(CV) regime. In quantum information science, the understanding andcharacterization of central resources such as entanglement may strongly rely onthe knowledge of the Gaussian or non-Gaussian character of the quantum state.However, the quantum measurement associated with the spectral photocurrent oflight modes consists of a mixture of quadrature observables. Within theframework 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 spectralphotocurrent relates to the character of the Wigner function describing thosemodes. We show that a Gaussian state can be misidentified as non-Gaussian andvice-versa, a conclusion that forces the adoption of tacit \textit{a priori}assumptions to perform quantum state reconstruction. We experimentally analyzethe light beams generated by the optical parametric oscillator (OPO) operatingabove threshold to show that the data strongly supports the generation ofGaussian states of the field, validating the use of necessary and sufficientcriteria to characterize entanglement in this system.

Analyzing the Gaussian character of the spectral quantum state of light via quantum noise measurements