Bell inequalities from multilinear contractions
Abstract
We provide a framework for Bell inequalities which is based on multilinear contractions. The derivation of the inequalities allows for an intuitive geometric depiction and their violation within quantum mechanics can be seen as a direct consequence of non-vanishing commutators. The approach is motivated by generalizing recent work on non-linear inequalities which was based on the moduli of complex numbers, quaternions and octonions. We extend results on Peres conjecture about the validity of Bell inequalities for quantum states with positive partial transposes. Moreover, we show the possibility of obtaining unbounded quantum violations albeit we also prove that quantum mechanics can only violate the derived inequalities if three or more parties are involved.
Cite
@article{arxiv.1002.1893,
title = {Bell inequalities from multilinear contractions},
author = {Alejo Salles and Daniel Cavalcanti and Antonio Acín and David Pérez-García and Michael M. Wolf},
journal= {arXiv preprint arXiv:1002.1893},
year = {2010}
}
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Published version