Bernstein's paradox of entangled quantum states

Bernstein's classical paradox of a regular colored-faced tetrahedron, while designed to illustrate the subtleties of probability theory, is strongly flawed in being asymmetric. Faces of tetrahedron are nonequivalent: three of them are single-colored, and one is many-colored. Therefore, even prior to formal calculations, a strong suspicion as to the independence of the color resulting statistics arises. Not so with entangled quantum states. In the schematic solutions proposed, while photon detection channels are completely symmetric and equivalent, the events that occur in them turn out to be statistically dependent, making the Bernstein paradox even more impressive due to the unusual behavior of quantum particles not obeying classical laws. As an illustrative example of the probability paradox, Greenberger–Horne–Zeilinger multiqubit states are considered.