Greenberger-Horne-Zeilinger theorem for N-partite quDits
We generalize Greenberger-Horne-Zeilinger (GHZ) theorem to an arbitrary number of D-dimensional systems. Contrary to conventional approaches, we use concurrent observables, which are incompatible but still have a common eigenstate. We begin with the theorem for 4 systems of a dimension divisible by 3, and discuss its extension to N systems of an arbitrary dimension. The GHZ theorem can be proved as long as N is not divisible by all non-unit divisors of D, smaller than N.