  Highly nonclassical character of optical quantum detectors, such as
single-photon detectors, is essential for preparation of quantum states of
light and a vast majority of applications in quantum metrology and quantum
information processing. Therefore, it is both fundamentally interesting and
practically relevant to investigate the nonclassical features of optical
quantum measurements. Here we propose and experimentally demonstrate a
procedure for direct certification of quantum non-Gaussianity and Wigner
function negativity, two crucial nonclassicality levels, of photonic quantum
detectors. Remarkably, we characterize the highly nonclassical properties of
the detector by probing it with only two classical thermal states and a vacuum
state. We experimentally demonstrate the quantum non-Gaussianity of
single-photon avalanche diode even under the presence of background noise, and
we also certify the negativity of the Wigner function of this detector. Our
results open the way for direct benchmarking of photonic quantum detectors with
a few measurements on classical states.
