Fidelity measure and conservation of information in general probabilistic theories

Abstract

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 information-theoretical 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.