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We implement a direct detection scheme based on hybrid photodetectors toexperimentally investigate high-order correlations for detected photons bymeans of quantities that can be experimentally accessed. We show theirusefulness in fully characterizing a multimode twin-beam state in comparisonwith classical states and, in particular, we introduce a nonclassicalitycriterion based on a simple linear combination of high-order correlationfunctions. Our scheme is self-consistent, allowing the estimation of all theinvolved parameters (quantum efficiency, number of modes and average energy)directly from the same experimental data. Results are in very good agreementwith theory, thus suggesting the exploitation of our scheme for reliable statecharacterization in quantum technology.

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