Looking for symmetric Bell inequalities

Authors:Jean-Daniel Bancal, Nicolas Gisin, Stefano Pironio
Journal:Journal of Physics A: Mathematical and Theoretical 43, 385303 (2010)
DOI:http://dx.doi.org/10.1088/1751-8113/43/38/385303
Abstract:Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins–Gisin–Linden–Massar–Popescu type.
File:bancal2010a.pdf

BibTeX Source

@article{1751-8121-43-38-385303,
  author={Jean-Daniel Bancal and Nicolas Gisin and Stefano Pironio},
  title={Looking for symmetric Bell inequalities},
  journal={Journal of Physics A: Mathematical and Theoretical},
  volume={43},
  number={38},
  pages={385303},
  url={http://stacks.iop.org/1751-8121/43/i=38/a=385303},
  year={2010},
  doi={10.1088/1751-8113/43/38/385303},
  abstract={Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins–Gisin–Linden–Massar–Popescu type.}
}