  We implement a direct detection scheme based on hybrid photodetectors to
experimentally investigate high-order correlations for detected photons by
means of quantities that can be experimentally accessed. We show their
usefulness in fully characterizing a multimode twin-beam state in comparison
with classical states and, in particular, we introduce a nonclassicality
criterion based on a simple linear combination of high-order correlation
functions. Our scheme is self-consistent, allowing the estimation of all the
involved parameters (quantum efficiency, number of modes and average energy)
directly from the same experimental data. Results are in very good agreement
with theory, thus suggesting the exploitation of our scheme for reliable state
characterization in quantum technology.
