  Entanglement and interference are both hallmark effects of quantum physics.
Particularly rich dynamics arise when multiple (at least partially)
indistinguishable particles are subjected to either of these phenomena. By
combining both entanglement and many-particle interference, we propose an
interferometric setting through which N-particle interference can be observed,
while any interference of lower orders is strictly suppressed. We
experimentally demonstrate this effect in a four-photon interferometer, where
the interference is nonlocal, in principle, as only pairs of photons interfere
at two separate and independent beam splitters. A joint detection of all four
photons identifies a high-visibility interference pattern varying as a function
of their collective four-particle phase, a genuine four-body property.
