  Quantum attributes of light have been related to non-classicality so far, i.
e. to incompatibility with mixtures of coherent states. The progress in quantum
optics indicates that this feature does not suffice to witness exotic behavior
of light. Contrary, quantum non-Gaussianity is starting to appear as a
promising and applicable property reflecting interesting states of light that
are suitable for quantum protocols. We investigate a newly introduced hierarchy
of criteria of quantum non-Gaussianity and predict this attribute can be
observed on light emitted from many single photon emitters, even if the light
undergoes realistic optical losses. It contrasts negativity of Wigner function,
that is unreachable in experimental platforms with losses above fifty percent.
