Classical no-cloning under Liouville dynamics by non-Csiszár f-divergence

Abstract. The Csiszár f-divergence, which is a class of information distance, is known to offer the classical counterpart of the quantum impossible cloning operations for the factrized and marginality classical probability distributions under Liouville dynamics. We show that a class of information distance belonging not to this divergence class also provides the classical version of the no-cloning processes. We address the nonlinear Liouville equations and generic distances to obtain the constraints against the functional forms which satisfy the classical version of that theorem.