  We experimentally verify the quantum non-Gaussian character of a
conditionally generated noisy squeezed single-photon state with positive Wigner
function. Employing an optimized witness based on probabilities of squeezed
vacuum and squeezed single-photon states we prove that the state cannot be
expressed as a mixture of Gaussian states. In our experiment, the non-Gaussian
state is generated by conditional subtraction of a single photon from squeezed
vacuum state. The state is probed with a homodyne detector and the witness is
determined by averaging a suitable pattern function over the measured homodyne
data. Our experimental results are in good agreement with a theoretical fit
obtained from a simple yet realistic model of the experimental setup.
