General Correlation Functions of the Clauser-Horne-Shimony-Holt Inequality for Arbitrarily High-Dimensional Systems

2003/06/30 by Libin Fu, Li-Bin Fu · 7 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.1103/physrevlett.92.130404

published as Phys. Rev. Lett. 92, 130404 (2004) · 4 pages, accepted by Phys. Rev. Lett

arxiv created 2004/02/13 · openalex publication_date 2004/03/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 dimensions. 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 of 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 by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]].

Citations

• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• On the Einstein Podolsky Rosen paradox

Cited by

• Entanglement detection via the condition of quantum correlation
• Violating Bell inequalities maximally for twod-dimensional systems
• Singularities of Berry connections inhibit the accuracy of the adiabatic approximation
• Multicomponent Bell inequality and its violation for continuous-variable systems
• Tight correlation-function Bell inequality for multipartited-dimensional systems
• Two-setting Bell inequalities for many qubits
• Gisin's Theorem for Three Qubits

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