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The Cohomology of Non-Locality and Contextuality · Around

2011

The Cohomology of Non-Locality and Contextuality

Abramsky, Samson, Mansfield, Shane, Barbosa, Rui Soares

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In a previous paper with Adam Brandenburger, we used sheaf theory to analyze the structure of non-locality and contextuality.

Moreover, on the basis of this formulation, we showed that the phenomena of non-locality and contextuality can be characterized precisely in terms of obstructions to the existence of global sections.
Our aim in the present work is to build on these results, and to use the powerful tools of sheaf cohomology to study the structure of non-locality and contextuality.
We use the Cech cohomology on an abelian presheaf derived from the support of a probabilistic model, viewed as a compatible family of distributions, in order to define a cohomological obstruction for the family as a certain cohomology class.

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