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Unbounded violations of bipartite Bell Inequalities via Operator Space theory

Villanueva, Ignacio and Junge, Marius and Pérez García, David and Wolf, Michael and Palazuelos Cabezón, Carlos (2010) Unbounded violations of bipartite Bell Inequalities via Operator Space theory. Communications in Mathematical Physics, 300 (3). pp. 715-739. ISSN 0010-3616

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Official URL: http://link.springer.com/article/10.1007/s00220-010-1125-5

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Abstract

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order Ω(√n∕Log2n) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative Lp embedding theory.
As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.


Item Type:Article
Uncontrolled Keywords:Banach-spaces; Quantum entanglement
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:10961
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