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Boole-Bell-Type inequalities in Mathematica

S. Filipp
Organization: Atominstitut der Österreichischen Universitäten
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The violation of Bell-type inequalities by the quantum probabilities represents an important aspect of quantum mechanics which is linked to the mind-boggling quantum features of nonlocality, complementarity and contextuality. Formally, such bounds on the classical probabilities from consistency arguments have already been investigated by Boole in the middle of the nineteenth century, termed "conditions of possible experience".

Boole-Bell-type inequalities can be found via correlation polytopes introduced by I. Pitowsky by utilizing the Minkowski-Weyl representation theorem and solving the hull problem. We introduce CddIF, a Mathematica package to compute all the Boole-Bell-type inequalities associated with an arbitrary physical setup. This package acts as an interface between Mathematica and the cdd program by Komei Fukuda, which represents a highly efficient method to solve the hull problem for general classical correlation polytopes.

A manual how to use this package is available at the e-print archive: quant-ph/0105083.

All files necessary to process CddIF in an MS Windows environment can be found here.

*Science > Physics > Quantum Physics

Bell inequalities, correlation polytopes, Minkowsky-Weyl representation theorem, probability theory
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*Boole-Bell-type inequalities in Mathematica   [in Articles]
*Boole-Bell-type inequalities in Mathematica   [in Conference Proceedings]
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cddif.m (36.5 KB) - Mathematica Package