  Light is an essential tool for connections between quantum devices and for
diagnostic of processes in quantum technology. Both applications deal with
advanced nonclassical states beyond Gaussian coherent and squeezed states.
Current development requires a loss-tolerant diagnostic of such nonclassical
aspects. We propose and experimentally verify a faithful hierarchy of genuine
$n$-photon quantum non-Gaussian light. We conclusively witnessed 3-photon
quantum non-Gaussian light in the experiment. Measured data demonstrates a
direct applicability of the hierarchy for a large class of real states.
