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Unbounded violation of tripartite Bell inequalities

Villanueva, Ignacio and Junge, Marius and Pérez García, David and Wolf, Michael and Palazuelos Cabezón, Carlos (2008) Unbounded violation of tripartite Bell inequalities. Communications in Mathematical Physics , 279 (2). pp. 455-486. ISSN 0010-3616

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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 commu-
nication 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 will
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.

Item Type:Article
Uncontrolled Keywords:Banach-spaces, Quantum entanglement, Summing operators, Tensor-products, Q-algebra, Theorem, Polynomials, States, Extensions, Forms
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:10913
Deposited On:29 Jun 2010 09:31
Last Modified:13 Dec 2013 17:46

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