Title: Categorical Probabilistic Theories,
Abstract: We present a simple categorical framework for the treatment of probabilistic
theories, with the aim of reconciling the fields of Categorical Quantum
Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years,
both CQM and OPTs have found successful application to a number of areas in
quantum foundations and information theory: they present many similarities,
both in spirit and in formalism, but they remain separated by a number of
subtle yet important differences. We attempt to bridge this gap, by adopting a
minimal number of operationally motivated axioms which provide clean
categorical foundations, in the style of CQM, for the treatment of the problems
that OPTs are concerned with.