 The three variants of Bell’s Theorem considered so far in this section concern ensembles of pairs of particles. An entirely new domain of variants is opened by studying ensembles of \(n\)-tuples of particles with \(n \ge 3\). The prototype of this kind of theorem was demonstrated by Greenberger, Horne, and Zeilinger (1989) (GHZ) for \(n=4\) and modified to \(n=3\) by Mermin (1990) and by Greenberger, Horne, Shimony, and Zeilinger (1990) (GHSZ). In the theorem of GHZ an entangled quantum state was written for four spin-\(\frac{1}{2}\) particles and the expectation value of the product of certain binary measurements performed on the individual particles was calculated. They then showed that the attempt to duplicate this expectation value subject to the factorizability constraint (F) produces a contradiction. A similar result was obtained by Mermin for a state of 3 spin-\(\frac{1}{2}\) particles and by GHSZ for a state of 3 photons entangled with respect to their direction of propagation. Because of the length of these arguments and limitations of space in the present article the details will not be summarized here, it is however worth mentioning that experimental tests were realized (Pan et al. 2000, Genovese 2005) (also in this case with additional hypotheses).