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Unbounded violation of tripartite Bell inequalities



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Villanueva, Ignacio y Junge, Marius y Pérez García, David y Wolf, Michael y 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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URL Oficial: http://www.springer.com/physics/journal/220


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.

Tipo de documento:Artículo
Palabras clave:Banach-spaces, Quantum entanglement, Summing operators, Tensor-products, Q-algebra, Theorem, Polynomials, States, Extensions, Forms
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:10913
Depositado:29 Jun 2010 09:31
Última Modificación:04 Dic 2014 11:01

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