Speaker
Amin Karamlou, University of Oxford
Title
Some Structural Aspects of Quantum Advantage
Abstract
This talk concerns the resource theory of contextuality. I first discuss the categorical account of this resource theory in terms of simulations between empirical models in the sheaf theoretic framework for contextuality. I then describe an equivalent characterisation of this category in the graph theoretic framework. This equivalence suggests that tools from either framework can be used to study simulations arising in quantum theory and beyond. In the second half the talk I will focus on the idea of self-testing which has proven to be an important tool in many recent results regarding quantum advantage. I propose a definition of self-testing in the sheaf theoretic framework. Using the idea of simulations between empirical models I then set out to find sufficient conditions under which the existence of one self-test implies the existence of another related one. Work in progress suggests that this idea can be used to prove novel self-testing results for certain synchronous non-local games. Examples include instances of the graph isomorphism and homomorphism games that are related to the magic square and magic pentagram constructions.
