Greenberger-Horne-Zeilinger paradoxes with symmetric multiport beam splitters

Abstract

In a gedankenexperiment N particles in a generalized GHZ-type beam entangled state (each particle can be in one of M beams) are fed into N symmetric 2M-port beam splitters (spatially separated). Correlation functions for such a process (using the Bell numbers value assignment approach) reveal a remarkable symmetry. For N=M+1 greater or equal to 4 a series of GHZ paradoxes are shown.