  Bosonic interference is a fundamental physical phenomenon, and it is believed
to lie at the heart of quantum computational advantage. It is thus necessary to
develop practical tools to witness its presence, both for a reliable assessment
of a quantum source and for fundamental investigations. Here we describe how
linear interferometers can be used to unambiguously witness genuine n-boson
indistinguishability. The amount of violation of the proposed witnesses bounds
the degree of multi-boson indistinguishability, for which we also provide a
novel intuitive model using set theory. We experimentally implement this test
to bound the degree of 3-photon indistinguishability in states we prepare using
parametric down-conversion. Our approach results in a convenient tool for
practical photonic applications, and may inspire further fundamental advances
based on the operational framework we adopt.
