Title: Sheaf theoretic structure of contextuality
Abstract: In this talk, I will present Abramsky and Brandenburger’s sheaf-theoretic framework of non-locality and contextuality in quantum theory. We will begin by setting up the mathematical framework of sheaf theory and empirical models. I will present in detail the central theorem, which gives a correspondence between the existence of local hidden variables, at the ontological model and the empirical model having a global section, at the operational level.
We will use Bell’s model as our running example to exhibit the non-existence of the global section using linear algebraic methods. We will see how this framework leads to a hierarchy of no-go theorems in quantum theory. The formalism presented here applies to any compatible empirical model (quantum theory being one of them), and thus has applications in topics beyond quantum. Time permitting, we will comment on a couple of them.
