Closed sets of nonlocal correlations

@article{Allcock2009ClosedSO,
  title={Closed sets of nonlocal correlations},
  author={Jonathan Allcock and Nicolas Brunner and Noah Linden and Sandu Popescu and Paul Skrzypczyk and Tam{\'a}s V{\'e}rtesi},
  journal={Physical Review A},
  year={2009},
  volume={80},
  pages={062107}
}
We present a fundamental concept - closed sets of correlations - for studying nonlocal correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for… 

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References

SHOWING 1-10 OF 17 REFERENCES
Phys
  • Rev. Lett. 102, 160403
  • 2009
Phys
  • Rev. Lett. 98, 010401
  • 2007
Phys
  • Rev. Lett. 88, 230406
  • 2002
Phys
  • Rev. A 77, 062109
  • 2008
Found
  • C. Ross
  • Medicine
    The Dental register
  • 1869
Phys
  • Rev. A 73, 012112 (2006); H. Barnum et al., Phys. Rev. Lett. 99, 240501
  • 2007
Phys
  • Rev. Lett. 102, 110402
  • 2009
Rohrlich , Found
  • Phys . Rev . A
Phys
  • Rev. Lett. 102, 180502
  • 2009
Phys
  • Rev. Lett. 67, 661
  • 1991
...
...