Dartmouth Events

A Greenberger-Horne-Zeilinger (GHZ) contradiction may be thought of as a
sequence of measurements whose outcomes can be described by hidden variables
up to, but not including the last measurement. The GHZ theorem differs from
the earlier Bell's theorem in that this quantum prediction for the last measurement
is definite (thus satisfying the Einstein-Podolsky-Rosen condition as an "element
of reality") while Bell's quantum prediction is probabilistic. We will show that
generalized GHZ states have a many-particle rotational symmetry that guarantees
the existence of contradictions for any number of particles (N > 3) of any spin.
While it is easy to show that hidden variables fail the rotational symmetry test for
any such system, the derivation of specific, experimentally verifiable contradictions
covering all cases has proven challenging. It is only recently that the most stubborn
cases have succumbed to the rotational symmetry arguments [PRA 89, 012105
(2014)].