Abstract

It is part of information theory folklore that, while quantum theory prohibits the generic cloning of states, such cloning is allowed by classical information theory. Indeed, many take the phenomenon of no-cloning to be one of the features that distinguishes quantum mechanics from classical mechanics. In this paper, we use symplectic geometry to argue that pace conventional wisdom, in the case where one does not include a machine system, there is an analog of the no-cloning theorem for classical systems. However, upon adjoining a non-trivial machine system one finds that, pace the quantum case, the obstruction to cloning disappears for pure states. We then discuss the difference between this result and the quantum case, and show that it can be explained in terms of the rigidity of the theories' respective geometries. Finally, we discuss the relationship between this result and classical no-cloning arguments in the context of symmetric monoidal categories and statistical classical mechanics.