Operational Theories of Physics as Categories

Abstract

We introduce a new approach to the study of operational theories of physics using category theory. We define a generalisation of the (causal) operational-probabilistic theories of Chiribella et al. and establish their correspondence with our new notion of an operational category. Our work is based on effectus theory, a recently developed area of categorical logic, to which we give an operational interpretation, demonstrating its relevance to the modelling of general probabilistic theories.