The validity domain, within quantum mechanics, of a full set of eight Bell inequalities for four observables is determined and represented geometrically. It turns out that the incorporation of all inequalities increases considerably the domain of invalidity. For special spin constellations, the validity regions become arbitrarily small. The results are compared with experiment and used to elucidate the status of the existing experimental evidence in favor of quantum theory and against hidden variables.

• Received 30 November 1992

DOI:https://doi.org/10.1103/PhysRevA.47.4627