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Quantum Violation: Beyond Clauser-Horne-Shimony-Holt Inequality

Hoshang Heydari
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Abstract

The best upper bound for the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality was first derived by Tsirelson. For increasing number of $\pm 1$ valued observables on both sites of the correlation experiment, Tsirelson obtained the Grothendieck's constant ($\mathcal{K}_{G}\approx 1.73\pm0.06$) as a limit for the maximal violation. In this paper, we construct a generalization of the CHSH inequality with four $\pm 1$ valued observables on both sites of a correlation experiment and show that the quantum violation approaching 1.58. Moreover, we estimate the maximal quantum violation of a correlation experiment for large and equal number of $\pm 1$ valued observables on both sites. In this case, the maximal quantum violation converges to $\sqrt{3}\approx1.73$ for very large $n$, which coincides with the approximate value of Grothendieck's constant.

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Hoshang Heydari. 2006-03-07. Quantum Violation: Beyond Clauser-Horne-Shimony-Holt Inequality. https://doi.org/10.1088/0305-4470/39/38/012

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