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On Bell-type inequalities. (English) Zbl 1213.81019
Summary: A Bell-type inequality is defined as an inequality of the type \(0\leq L\leq 1\), where \(L\) is a linear combination with real coefficients of probabilities \(p_i\) and joint probabilities \(p_{ij}, p_{ijk},\dots\), \(p_{l,\dots,n}\) corresponding to \(n\) events. A general theorem on the validity of such inequalities in correspondence to physical assumptions about commutativity or noncommutativity is given. Examples and possible physical applications are discussed.

81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
Full Text: DOI
[1] G. Boole,Philos. Trans. R. Soc. London 152, 225 (1862). · Zbl 1319.60004
[2] I. Pitowsky,Quantum Probability–Quantum Logic (Lecture Notes in Physics, Vol. 321) (Springer, New York, 1969). · Zbl 0668.60096
[3] E. G. Beltrametti and M. J. Maczynski,J. Math. Phys. 32, 1280 (1991);34, 4919 (1993). · Zbl 0731.60003
[4] J. S. Bell,Physics 1, 195 (1964).
[5] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt,Phys. Rev. Lett. 23, 880 (1969). · Zbl 1371.81014
[6] R. Sikorski,Boolean Algebras (Springer, New York 1964).
[7] C. Del Noce, Thesis, Department of Physics, University of Genoa, 1993.
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