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Quantum non-Gaussian states represent an important class of highlynon-classical states whose preparation requires quantum operations ormeasurements beyond the class of Gaussian operations and statistical mixing.Here we derive criteria for certification of quantum non-Gaussianity based onprobability of vacuum in the original quantum state and a state transmittedthrough a lossy channel with transmittance T. We prove that the criteria holdfor arbitrary multimode states, which is important for their applicability inexperiments with broadband sources and single-photon detectors. Interestingly,our approach allows to detect quantum non-Gaussianity using only onephotodetector instead of complex multiplexed photon detection schemes, at thecost of increased experimental time. We also formulate a quantumnon-Gaussianity criterion based on the vacuum probability and mean photonnumber of the state and we show that this criterion is closely related to thecriteria based on pair of vacuum probabilities. We illustrate the performanceof the obtained criteria on the example of realistic imperfect single-photonstates modeled as a mixture of vacuum and single-photon states with backgroundPoissonian noise.

Quantum non-Gaussianity criteria based on vacuum probabilities of original and attenuated state