Bell inequalities from multilinear contractions

TY - JOUR

T1 - Bell inequalities from multilinear contractions

AU - Salles, Alejo

AU - Cavalcanti, D.

AU - Acin, A.

AU - Perez-Garcia, D.

AU - Wolf, Michael Marc

PY - 2010/7/1

Y1 - 2010/7/1

N2 - 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.

AB - 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.

M3 - Journal article

SN - 1533-7146

VL - 10

SP - 703

EP - 719

JO - Quantum Information and Computation

JF - Quantum Information and Computation

IS - 7-8

ER -