Simulations between contextual resources
We describe a resource theory for contexuality in two ways and prove them to be equivalent. The two viewpoints are given by (i) starting with a very simple notion of an empirical model simulating another one and then extending it to a more useful notion by passing over to a co-Kleisli category, and (ii) considering free algebraic operations that transform empirical models to other empirical models. These viewpoints capture various notions of intraconversions between correlations that have been studied in the literature on non-locality. An advantage of having a rigorous theory of such intraconversions is in new techniques suggested by the approach: a case in point is a no-cloning/no-broadcasting theorem which states that an empirical model can simulate two independent copies of itself iff it is non-contextual. If time permits, we will discuss ongoing work and further questions suggested by the framework.