Bell inequalities with a magnitude of violation that grows exponentially with the number of particles

Abstract

A simple Bell inequality for an n-particle system in a Greenberger-Horne-Zeilinger state is derived. Quantum mechanics violates this inequality by an exponentially large factor of $2^{\left(\mathit{n}\mathrm{-}2\right)/2}$ for n odd or $2^{\left(\mathit{n}\mathrm{-}1\right)/2}$ for n even.