Quantum reference frames in relational quantum theory: finite dimensional groups

I will motivate the relational approach to physics and contrast to the “external” perspective. I will argue that relational states should be understood as encoding some symmetry transformations (and superpositions thereof for quantum states). I will extend an existing reference frame transformation (for the translation group) defined for relational quantum theory to finite groups. I will contrast the reference change defined in the talk to the standard (external) approach used in quantum information. Following this I will discuss potential applications of the change of reference frame such as Wigner’s friend. This is very much work in progress.