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Derivation of the full set of Bell inequalities involving correlation functions, for two parties, with binary observables, and N possible local settings is not as easy as it seemed. The proof of v1 is wrong. Additionaly one can find a counterexample, which will be presented soon. Thus our thesis is dead. Still the series of Bell inequalities discussed in the manuscript (v1) form a necessary condition for local realism, and are tight. They are tight and complete (sufficient) only for N=3 settings per observer (as shown in quant-ph/0611086, fortunately using an entirely different approach).
Bells inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local hidden variables that might affect the outcomes of measurements on entangled particles. This assumption ha
A method for construction of the multipartite Clauser-Horne-Shimony-Holt (CHSH) type Bell inequalities, for the case of local binary observables, is presented. The standard CHSH-type Bell inequalities can be obtained as special cases. A unified frame
In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two partite system, Alice and Bob each make one of
Bell inequality with self-testing property has played an important role in quantum information field with both fundamental and practical applications. However, it is generally challenging to find Bell inequalities with self-testing property for multi
For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the probability of random $N$-qu$d$it pure states to substantially violate any Bell inequality with uniformly bounded coefficients. We prove that under some cond