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Two-Setting Bell Inequalities for Many Qubits
Kai Chen, Sergio Albeverio and Shao-Ming Fei
We present a family of tight Bell inequalities involving only two measurement settings of each party for $N>2$ qubits. All the Greenberger-Horne-Zeilinger states of $N$ qubits (up to local unitary transformations) are shown to violate the inequalities maximally, by an amount that grows exponentially with $N$. Remarkably our new inequalities are violated by some states which do satisfy all the standard Bell inequalities.Furthermore the inequalities automatically recover all the standard ones for systems less than $N$ qubits. Their implementations are not only favorably within the reach of well-established technology of linear optics, but also can provide stronger nonlocality tests and contribute significantly to the reduction of experimental efforts.