Twirled and swirled worlds: a compositional approach

arXiv:2610.33294v1 Announce Type: new Abstract: Twirled and swirled worlds describe generalised probabilistic theories (GPTs) restricted by symmetry-imposed superselection rules. We extend these constructions to a fully compositional setting for finite-dimensional GPTs and compact groups, treating states, effects, and multipartite transformations uniformly as processes. We distinguish system actions from process-space actions. We define actions on a theory as a whole by requiring the corresponding process-space actions to respect sequential and parallel composition. Averaging physical theory actions defines twirling, while averaging nonphysical theory actions defines swirling.