Bell-type inequalities in orthomodular lattices. I: Inequalities of order 2
The authors study Bell-type inequalities in orthomodular lattices and concentrate their attention on inequalities of order 2. They give several characterizations of the original Bell inequality (in particular, they show that it implies all Bell-type inequalities of order 2) and study Bell-type inequalities in structures connected with a Hilbert space. They characterize Boolean algebras by means of properties of the set of states fulfilling the Bell inequality -- they generalize results of \textit{S. Pulmannová} and \textit{V. Majerník} [J. Math. Phys. 33, 2173-2178 (1992; Zbl 0771.03022)] and of \textit{P. Pták} and \textit{S. Pulmannová} [Commentat. Math. Univ. Carol. 35, 205-208 (1994; Zbl 0805.06010)].
scientific article; zbMATH DE number 800573
scientific article