RT Journal Article
T1 Unbounded violation of tripartite Bell inequalities
A1 Pérez García, David
A1 Wolf, Michael
A1 Palazuelos Cabezón, Carlos
A1 Villanueva Díez, Ignacio
A1 Junge, Marius
AB We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. In order to derive all these physical consequences, we wil have to obtain new mathematical results in the theories of operator spaces and tensor norms. In particular, we will prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.
PB Springer
SN 0010-3616
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/49393
UL https://hdl.handle.net/20.500.14352/49393
LA eng
NO Pérez García, D., Wolf, M., Palazuelos Cabezón, C., Villanueva Díez, I. et al. «Unbounded Violation of Tripartite Bell Inequalities». Communications in Mathematical Physics, vol. 279, n.o 2, abril de 2008, pp. 455-86. DOI.org (Crossref), https://doi.org/10.1007/s00220-008-0418-4.
DS Docta Complutense
RD 8 abr 2025