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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343kB |

Official URL: http://www.springer.com/physics/journal/220

## Abstract

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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