Looking for symmetric Bell inequalities

Article, Preprint English OPEN
Bancal, Jean-Daniel ; Gisin, Nicolas ; Pironio, Stefano (2010)
  • Journal: Journal of Physics A: Mathematical and Theoretical (issn: 1751-8113)
  • Related identifiers: doi: 10.1088/1751-8113/43/38/385303
  • Subject:
    • ddc: ddc:500.2
    arxiv: Quantum Physics | High Energy Physics::Experiment

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.
  • References (4)

    [1] I. Pitowsky, Quantum Probability { Quantum Logic (Springer-Verlag, 1989).

    [2] J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, 1987).

    [3] A. Aspect, Nature 398, 189 (1999).

    [4] S. Pironio, A. Acin, N. Brunner, N. Gisin, S. Massar, V. Scarani, New J. Phys. 11, 045021 (2009).

  • Metrics
    1
    views in OpenAIRE
    0
    views in local repository
    0
    downloads in local repository
Share - Bookmark