We introduce and experimentally explore the concept of the 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.

Department of Optics Palacký University 17 listopadu 1192 12 771 46 Olomouc Czech Republic

Institut für Experimentalphysik Universität Innsbruck Technikerstraße 25 6020 Innsbruck Austria

Joint Quantum Institute National Institute of Standards and Technology and University of Maryland Gaithersburg Maryland 20849 USA

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