We investigate the main features of a measure of fidelity between states in a general family of probabilistic theories admitting classical probability theory and standard quantum theory as particular instances. We apply the aforementioned measure to investigate informationtheoretical
features of these theories related to the conservation of information during the evolution
of closed physical systems. In particular, we derive a generalization of a fundamental result in
quantum theory relevant for the measurement problem: Zurek’s recent extension of the no-cloning theorem.