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

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.