  We report the experimental reconstruction of a nonclassicality
quasiprobability for a single-photon added thermal state. This quantity has
significant negativities, which is necessary and sufficient for the
nonclassicality of the quantum state. Our method presents several advantages
compared to the reconstruction of the P function, since the nonclassicality
filters used in this case can regularize the quasiprobabilities as well as
their statistical uncertainties. A-priori assumptions about the quantum state
are therefore not necessary. We also demonstrate that, in principle, our method
is not limited by small quantum efficiencies.
