Issue
EPL
Volume 83, Number 5, September 2008
Article Number 50007
Number of page(s) 4
Section General
DOI http://dx.doi.org/10.1209/0295-5075/83/50007
Published online 02 September 2008
EPL, 83 (2008) 50007
DOI: 10.1209/0295-5075/83/50007

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

T. Yamano and O. Iguchi

Department of Physics, Ochanomizu University - 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan

yamano@cosmos.phys.ocha.ac.jp
osamu@phys.ocha.ac.jp

received 4 March 2008; accepted in final form 18 July 2008; published September 2008
published online 2 September 2008

Abstract
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.

PACS
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.

© EPLA 2008