  Superposition is one of the most distinct features of quantum theory and has
been demonstrated in numerous realizations of Young's classical double-slit
interference experiment and its analogues. However, quantum entanglement - a
significant coherent superposition in multiparticle systems - yields phenomena
that are much richer and more interesting than anything that can be seen in a
one-particle system. Among them, one important type of multi-particle
experiments uses path-entangled number-states, which exhibit pure higher-order
interference and allow novel applications in metrology and imaging such as
quantum interferometry and spectroscopy with phase sensitivity at the
Heisenberg limit or quantum lithography beyond the classical diffraction limit.
Up to now, in optical implementations of such schemes lower-order interference
effects would always decrease the overall performance at higher particle
numbers. They have thus been limited to two photons. We overcome this
limitation and demonstrate a linear-optics-based four-photon interferometer.
Observation of a four-particle mode-entangled state is confirmed by
interference fringes with a periodicity of one quarter of the single-photon
wavelength. This scheme can readily be extended to arbitrary photon numbers and
thus represents an important step towards realizable applications with
entanglement-enhanced performance.
