  Quantum non-Gaussian states represent an important class of highly
non-classical states whose preparation requires quantum operations or
measurements beyond the class of Gaussian operations and statistical mixing.
Here we derive criteria for certification of quantum non-Gaussianity based on
probability of vacuum in the original quantum state and a state transmitted
through a lossy channel with transmittance T. We prove that the criteria hold
for arbitrary multimode states, which is important for their applicability in
experiments with broadband sources and single-photon detectors. Interestingly,
our approach allows to detect quantum non-Gaussianity using only one
photodetector instead of complex multiplexed photon detection schemes, at the
cost of increased experimental time. We also formulate a quantum
non-Gaussianity criterion based on the vacuum probability and mean photon
number of the state and we show that this criterion is closely related to the
criteria based on pair of vacuum probabilities. We illustrate the performance
of the obtained criteria on the example of realistic imperfect single-photon
states modeled as a mixture of vacuum and single-photon states with background
Poissonian noise.
