Quantum statistics
When two particles are incident symmetrically on a 50/50 beam splitter it is possible for both to emerge in either the same beam (left) or in different beams (right). In general, bosons (e.g. photons) emerge in the same beam, while fermions (e.g. electrons) emerge in different beams. The situation is more complex for entangled states, however, and two photons in the Bell state |Yñ emerge in different beams. Therefore, if detectors placed in the two outward directions register photons at the same time, the experimenter knows that they were in a |Yñ state. Moreover, because we do not know the paths followed by the photons, they remained entangled.