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Bell inequalities from multilinear contractions

Wolf, Michael and Pérez García, David and Salles, Alejo and Cavalcanti, Daniel and Acín, Antonio (2010) Bell inequalities from multilinear contractions. Quantum Information & Computation , 10 . ISSN 1533-7146

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Official URL: http://arxiv.org/abs/1002.1893

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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.

Item Type:Article
Uncontrolled Keywords:Física matemática, Teoría cuántica, Quantum Physics, Mathematical Physics
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:12158
Deposited On:03 Feb 2011 08:44
Last Modified:30 Aug 2011 12:00

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