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Minimal and maximal sets of Bell-type inequalities holding in a logic. (English) Zbl 0862.03040
Let \(p\) be a state on a quantum logic \(L\) (= orthomodular lattice). Let \(n\) be an integer, \(N=\{1,\dots,n\}\) and \(f:2^N\to Z\). A Bell-type inequality is an inequality \[ \sum_{I\subseteq N}f(I) p(\bigwedge_{i\in I}a_i)\in [0,1], \] \(a_1,\dots, a_n\in L\). The authors show that the class of all functions \(f:2^N\to Z\) which give a Bell-type inequality, has a smallest and a greatest element.
MSC:
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
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