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Phys. Rev. A 74, 062109 (2006) [8 pages]Bell inequality with an arbitrary number of settings and its applications
Koji Nagata,1,2 Wies
 aw Laskowski,1 and Tomasz Paterek1,31Instytut Fizyki Teoretycznej i Astrofizyki, Uniwersytet Gda  ski, PL-80-952 Gdask, Poland 2National Institute of Information and Communications Technology, 4-2-1 Nukuikita, Koganei, Tokyo 184-8795, Japan 3The Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Vienna, Austria
Received 16 January 2006; revised 6 June 2006; published 18 December 2006
Based on a geometrical argument introduced by ©2006 The American Physical Society
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ukowski, 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 nonseparable 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.
. Brukner, M. 
niak, 
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