Shane Mansfield

Oxford University, UK

Contextuality, Cohomology & Paradox

Abstract: Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Sheaf theory can be used to provide a general treatment of contextuality in quantum theory. However, contextual phenomena are found in other fields as well: for example, database theory. I will discuss my recent work in collaboration with Abramsky, Barbosa, Kishida & Lal (http://arxiv.org/abs/1502.03097) in which we develop this unified view of contextuality. This provides two main contributions: firstly, it exposes a remarkable connection between contexuality and logical paradoxes; secondly, an important class of contextuality arguments can be demonstrated to have a topological origin. More specifically, it is shown that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions