Greenberger-Horne-Zeilinger paradoxes for N N-dimensional systems

Abstract

The series of Greenberger-Horne-Zeilinger (GHZ)-like paradoxes for N maximally entangled quantum systems was discussed. The paradoxes were found to naturally split into two parts: the even and the odd number of observers and input ports. The hypothesis of local hidden variables lead to a prediction of perfect correlations. It was found that the multiport beam splitters and the idea of value assignment-based Bell numbers lead to the generalization of the GHZ paradox.