Greenberger-Horne-Zeilinger Paradox in Arbitrary Dimension

Abstract

We present a generalized Greenberger-Horne-Zeilinger (GHZ) paradox in a multipartite system witheach subsystem of arbitrary even dimension. Contrary to conventional approaches of compatibleobservables, in order to prove Bell’s theorem, we employ concurrent observables, that are mutually incompatible but still have a common eigenstate such that they are involved in elements of physicalreality. It is proved that our formulation of the generalized GHZ paradox is genuinely multidimensional. The present approach enables an m-partite system to exhibit the truly d-dimensional GHZ paradox for d even and m odd integers. As a special case it covers previous works which require a (d + 1)-partite system.