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arXiv · quant-ph/0601107

Bell inequality with an arbitrary number of settings and its applications

Koji Nagata·Wieslaw Laskowski·Tomasz Paterek
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Abstract

Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results. Moreover, a necessary and sufficient condition for the violation of this inequality is presented. It turns out that the class of non-separable states which do not admit local realistic description is extended when compared to the two-setting inequalities. However, supporting the conjecture of Peres, quantum states with positive partial transposes with respect to all subsystems do not violate the inequality. Additionally, we follow a general link between Bell inequalities and communication complexity problems, and present a quantum protocol linked with the inequality, which outperforms the best classical protocol.

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Koji Nagata, Wieslaw Laskowski, Tomasz Paterek. 2006-10-31. Bell inequality with an arbitrary number of settings and its applications. https://doi.org/10.1103/physreva.74.062109

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