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

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Li-Bin Fu

Quantum Physics · Submitted 16 Jun 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDquant-ph/0306102 (version 3)
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CitationLi-Bin Fu. "General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems." arXiv:quant-ph/0306102 (2003). https://pith.science/paper/GSKRQX7D
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arXiv listing abstract v3. Results and the main claim are underlined; .

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)].

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. contribution 1.00 0.94 0.29 asserted 1.00
s1 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. contribution 0.84 0.95 0.52 asserted 1.00
s2 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. result 0.79 0.79 0.28 asserted 0.97
s3 We also discuss the physical meaning and general definition of the correlation functions. contribution 0.78 0.84 0.05 asserted 0.82
s4 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)]. contribution 0.63 0.85 0.08 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper
Original 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)].

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