Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence

TL;DR

This paper extends the classical no-cloning theorem to Liouville dynamics using non-Csiszár f-divergences, revealing new constraints on classical information distances beyond traditional divergence classes.

Contribution

It introduces a novel class of information distances that support a classical no-cloning theorem under Liouville dynamics, beyond the Csiszár f-divergence framework.

Findings

Classical no-cloning theorem can be formulated with non-Csiszár f-divergences.

Constraints on the functional forms of information distances are derived.

The results apply to nonlinear Liouville-like equations.

Abstract

The Csisz\'ar 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 classical analogue of the no-cloning principle.