  We introduce and experimentally explore the concept of quantum non-Gaussian
depth of single-photon states with a positive Wigner function. The depth
measures the robustness of a single-photon state against optical losses. The
directly witnessed quantum non-Gaussianity withstands significant attenuation,
exhibiting a depth of 18 dB, while the nonclassicality remains unchanged.
Quantum non-Gaussian depth is an experimentally approachable quantity that is
much more robust than the negativity of the Wigner function. Furthermore, we
use it to reveal significant differences between otherwise strongly
nonclassical single-photon sources.
