  Particle indistinguishability is at the heart of quantum statistics that
regulates fundamental phenomena such as the electronic band structure of
solids, Bose-Einstein condensation and superconductivity. Moreover, it is
necessary in practical applications such as linear optical quantum computation
and simulation, in particular for Boson Sampling devices. It is thus crucial to
develop tools to certify genuine multiphoton interference between multiple
sources. Here we show that so-called Sylvester interferometers are near-optimal
for the task of discriminating the behaviors of distinguishable and
indistinguishable photons. We report the first implementations of integrated
Sylvester interferometers with 4 and 8 modes with an efficient, scalable and
reliable 3D-architecture. We perform two-photon interference experiments
capable of identifying indistinguishable photon behaviour with a Bayesian
approach using very small data sets. Furthermore, we employ experimentally this
new device for the assessment of scattershot Boson Sampling. These results open
the way to the application of Sylvester interferometers for the optimal
assessment of multiphoton interference experiments.
