  Path identiy induces a broad interest in recent years due to the foundation
for numerous novel quantum information applications. Here, we experimentally
demonstrate quantum coherent superposition of two different origins of a
four-photon state, where multi-photon frustrated interference emerges from the
quantum indistinguishability by path identity. The quantum state is created in
four probabilistic photon-pair sources on one integrated silicon photonic chip,
two combinations of which can create photon quadruplets. Coherent elimination
and revival of distributed four-photons are fully controlled by tuning phases.
The experiment gives rise to peculiar quantum interference of two possible ways
to create photon quadruplets rather than interference of different intrinsic
properties of photons. Besides many known potential applications, this new kind
of multi-photon nonlinear interference enables the possibility for various
fundamental studies such as nonlocality with multiple spatially separated
locations.
