Large Violation of Bell Inequalities with Low Entanglement

@article{Junge2011LargeVO,
  title={Large Violation of Bell Inequalities with Low Entanglement},
  author={Marius Junge and Carlos Palazuelos},
  journal={Communications in Mathematical Physics},
  year={2011},
  volume={306},
  pages={695-746}
}
In this paper we obtain violations of general bipartite Bell inequalities of order $${\frac{\sqrt{n}}{\log n}}$$ 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… 
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