Anyonic information theory and quantum foundations

In this talk, I present the latest works on anyonic information theory and how it is linked to aspects of quantum foundations

First, the theory of 2+1 D non-abelian anyons will be introduced. The newly discovered notion of anyonic creation operators will be presented, as well as their use as local elements of reality within the Deutsch-Hayden interpretation of quantum mechanics. The relationship between anyonic systems and quantum reference frames will be explored, concretely in the area of subsystem relativity.

Lastly, I will present the strange properties of anyonic entanglement, such as the different spectra of marginals in bipartite systems. This property makes the Von Neumann entropy a bad entanglement measure. I will explain the challenges of defining entanglement measures for anyonic systems and current approaches.