Abstract
We study Bell-type inequalities of ordern with emphasis on the casen = 2 in the framework of the structure of an orthomodular lattice, which is a logicoalgebraic model of quantum mechanics. We give necessary and sufficient conditions for the validity of Bell-type inequalities of order 2. In particular, we study Bell-type inequalities in various structures connected with a Hilert space, and we give a characterization of Boolean algebras via the validity of certain Bell-type inequalities.
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Dvurečenskij, A., Länger, H. Bell-type inequalities in orthomodular lattices. I. Inequalities of order 2. Int J Theor Phys 34, 995–1024 (1995). https://doi.org/10.1007/BF00671363
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DOI: https://doi.org/10.1007/BF00671363