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Bell inequalities for three systems and arbitrarily many measurement outcomes

Publication date2012
Abstract

We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin-Bell inequality. For a small number of outcomes, we verify that our inequalities define facets of the polytope of local correlations. We investigate the quantum violations of these inequalities, in particular with respect to the Hilbert space dimension. We provide strong evidence that the maximal quantum violation can be reached only using systems with local Hilbert space dimension exceeding the number of measurement outcomes. This suggests that our inequalities can be used as multipartite dimension witnesses.

Citation (ISO format)
GRANDJEAN, Basile et al. Bell inequalities for three systems and arbitrarily many measurement outcomes. In: Physical review, A, Atomic, molecular, and optical physics, 2012, vol. 85, n° 5. doi: 10.1103/PhysRevA.85.052113
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ISSN of the journal1050-2947
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