Two-Setting Bell Inequalities for Many Qubits

revised version: October 2006
Kai Chen, Sergio Albeverio, and Shao-Ming Fei
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Submission date: 22. Mar. 2006
Pages: 12
published in: Physical review / A, 74 (2006) 5, art-no. 050101 
DOI number (of the published article): 10.1103/PhysRevA.74.050101
PACS-Numbers: 03.65.Ud, 03.67.Mn, 42.50.-p
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Abstract:
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.