Quantum non-Gaussianity certification of photon-number-resolving detectors

We report on direct experimental certification of the quantum non-Gaussian character of a photon-number resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements $\hat{\Pi}_m$ associated with the $m$-fold coincidence counts, up to $m=7$. The experimental ability to certify from the first principles the quantum non-Gaussian character of $\hat{\Pi}_m$ is for large $m$ limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.