General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems

Abstract

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two-dimension. This inequality is optimal in the same sense as the CHSH inequality for two dimensional systems, namely, the maximal amount by which the inequality is violated consists with the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].

arXiv comment4 pages, accepted by Phys. Rev. Lett

References in corpus (6)

• Bell inequalities for arbitrarily high dimensional systems
• Violations of local realism by two entangled quNits are stronger than for two qubits
• Quantum non-locality in two three-level systems
• New optimal tests of quantum nonlocality
• Violations of local realism with quNits up to N=16
• Maximal violation of Clauser-Horne-Shimony-Holt inequality for two qutrits

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