Classical no-cloning theorem under Liouville dynamics by non-Csiszár f-divergenceT. Yamano and O. Iguchi
Department of Physics, Ochanomizu University - 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan
received 4 March 2008; accepted in final form 18 July 2008; published September 2008
published online 2 September 2008
The Csiszár f-divergence, which is a class of information distances, is known to offer a useful tool for analysing the classical counterpart of the cloning operations that are quantum-mechanically impossible for the factorized and marginality classical probability distributions under Liouville dynamics. We show that a class of information distances that does not belong to this divergence class also allows for the formulation of a classical analogue of the quantum no-cloning theorem. We address a family of nonlinear Liouville-like equations, and generic distances, to obtain constraints on the corresponding functional forms, associated with the formulation of a classical analogue of the no-cloning principle.
05.20.Gg - Classical ensemble theory.
05.90.+m - Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems.
89.70.-a - Information and communication theory.
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