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arXiv · 1112.2827

Homogenization of Bell inequalities

Yu-Chun Wu·Marek Żukowski
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Abstract

A technique, which we call homogenization, is applied to transform CH-type Bell inequalities, which contain lower order correlations, into CHSH-type Bell inequalities, which are defined for highest order correlation functions. A homogenization leads to inequalities involving more settings, that is a choice of one more observable is possible for each party. We show that this technique preserves the tightness of Bell inequalities: a homogenization of a tight CH-type Bell inequality is still a tight CHSH-type Bell inequality. As an example we obtain $3\times3\times3$ CHSH-type Bell inequalities by homogenization of $2\times 2\times 2$ CH-type Bell inequalities derived by Sliwa in [Phys. Lett. A {\bf 317}, 165 (2003)].

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Yu-Chun Wu, Marek Żukowski. 2011-12-13. Homogenization of Bell inequalities. https://doi.org/10.1103/physreva.85.022119

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