Measuring high-order photon-number correlations in experiments with multimode pulsed quantum states

We implement a direct detection scheme based on hybrid photodetectors to experimentally investigate high-order correlations for detected photons by means of experimentally accessible quantities. The scheme is self-consistent, allowing the estimation of all the involved parameters (quantum efficiency, number of modes, and average energy). In particular, we show how high-order correlation functions can be exploited to fully characterize bipartite multimode states in regimes realistic for quantum technology, that is, in the mesoscopic photon-number domain and with limited quantum efficiency. Furthermore, we introduce a nonclassicality criterion based on a simple linear combination of high-order correlation functions.