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Large Violation of Bell Inequalities with Low Entanglement

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Junge, M. and Palazuelos Cabezón, Carlos (2011) Large Violation of Bell Inequalities with Low Entanglement. Communications in Mathematical Physics , 306 (3). pp. 695-746. ISSN 0010-3616

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Official URL: http://link.springer.com/article/10.1007/s00220-011-1296-8


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http://arxiv.org/abs/1007.3043Organisation


Abstract

In this paper we obtain violations of general bipartite Bell inequalities of order root n/log n with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.


Item Type:Article
Uncontrolled Keywords:Communication complexity; operator-spaces; nonlocality; matrices; theorem
Subjects:Sciences > Physics > Mathematical physics
ID Code:24434
Deposited On:30 Jan 2014 11:38
Last Modified:07 Feb 2014 11:17

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