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Communications in Mathematical Physics

, Volume 300, Issue 3, pp 715–739 | Cite as

Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

  • M. Junge
  • C. Palazuelos
  • D. Pérez-García
  • I. Villanueva
  • M. M. Wolf
Article

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 \({{\rm \Omega} \left(\frac{\sqrt{n}}{\log^2n} \right)}\) 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 L p 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.

Keywords

Operator Space Bell Inequality Tensor Norm Complete Contraction Parallel Repetition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • M. Junge
    • 1
  • C. Palazuelos
    • 1
    • 2
  • D. Pérez-García
    • 2
  • I. Villanueva
    • 2
  • M. M. Wolf
    • 3
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignIllinoisUSA
  2. 2.Departamento de Análisis MatemáticoUniversidad Complutense de MadridMadridSpain
  3. 3.Niels Bohr InstituteCopenhagenDenmark

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