Abstract
We give a necessary and sufficient condition for a Bell-type inequality to hold in a horizontal sum of finitely many finite Boolean algebras.
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References
J. S. Bell, “On the Einstein-Podolsky-Rosen paradox”Physics 1, 195–200 (1964).
E. G. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1981).
E. G. Beltrametti and M. J. Maczyński, “On Bell-type inequalities,”Found. Phys. 24, 1153 (1994).
G. Birkhoff and J. von Neumann,The logic of quantum mechanics, Ann. Math. 37, 823–834 (1936).
D. Dorninger and W. B. Müller,Allgemeine Algebra und Andwedungen (Teubner, Stuttgart, 1984).
A. Dvurečenskij and H. Länger, “Bell-type inequalities in Orthomodular Lattices I. Inequalities of Order 2,”Int. J. Theor. Phys., submitted (1994).
J. M. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1968).
G. Kalmbach,Orthomodular Lattices (Academic Press, New York, 1983).
H. Länger and M. Maczyński, “On a characterization of probability measures on Boolean algebras and some orthomodular lattices,”Math. Slovaca, to appear.
G. W. Mackey,The Mathematical Foundations of Quantum Mechanics (Benjamin Reading, Massachusetts, 1963).
C. Piron,Foundations of Quantum Physics (Benjamin, Reading, Massachusetts, 1976).
I. Pitowsky,Quantum Probability-Quantum Logic (Lecture Notes in Physics, 321) (Springer, New York, 1989).
P. Pták and S. Pulmannová,Orthomodular Structures as Quantum Logics (Kluwer Academic, Dordrecht, 1991).
S. Pulmannová and V. Majerník, “Bell inequalities on quantum logics,”J. Math. Phys. 33, 2173–2178 (1992).
E. Santos, “The Bell inequalities as tests of classical logic,”Phys. Lett. A 115, 363–365 (1986).
V. S. Varadarajan,Geometry of Quantum Theory, Vol. 1 (Van Nostrand, Princeton, New Jersey, 1968).
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Dvurečenskij, A., Länger, H. Bell-type inequalities in horizontal sums of Boolean algebras. Found Phys 24, 1195–1202 (1994). https://doi.org/10.1007/BF02057864
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DOI: https://doi.org/10.1007/BF02057864