Bell inequalities for three systems and arbitrarily many measurement outcomes

Basile Grandjean*, Yeong-Cherng Liang, Jean-Daniel Bancal, Nicolas Brunner, Nicolas Gisin

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)


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.

Original languageEnglish
Article number052113
Number of pages6
JournalPhysical Review A: Atomic, Molecular and Optical Physics
Issue number5
Publication statusPublished - 17 May 2012




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