Extendability in the Sheaf-theoretic Approach: Construction of Bell Models from Kochen-Specker Models

Understand

Extendability of an empirical model was shown by Abramsky & Brandenburger to correspond in a unified manner to both locality and non-contextuality.

• We develop their approach by presenting a refinement of the notion of extendability that can also be useful in characterising the properties of sub-models.
• The refinement is found to have another useful application: it is shown that a particular canonical extension, when well-defined, may be used for the construction of Bell-type models from models of more general kinds in such a way that the constructed model is equivalent to the original in terms of non-locality/contextuality.
• This is important since on practical and foundational levels, the notion of locality in Bell-type models can more easily be motivated than the corresponding general notion of contextuality.