A sequence of Bell inequalities for N-particle systems, which involve three settings of each of the local measuring apparatuses, is derived. For Greenberger-Horne-Zellinger states, quantum mechanics violates these inequalities by factors exponentially growing with N. The threshold visibilities of the multiparticle sinusoidal interference fringes, for which local realistic theories are ruled out, decrease as (2/3)N.
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Żukowski et al. (1997) studied this question.
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