A physical perspective on classical cloning

Highlights: • Quadratic Hamiltonians for classical cloning. • Nonlinear optics experiment proposed to realise classical cloning. • Corruption of cloning by thermal noise. • New examples of cloning maps on manifolds. • Proof that phase spaces over group manifolds admit minimal cloning maps. -- Abstract: The celebrated quantum no-cloning theorem states that an arbitrary quantum state cannot be cloned perfectly. This raises questions about cloning of classical states, which have also attracted attention. Here, we present a physical approach to the classical cloning process showing how cloning can be realised using Hamiltonians. After writing down a canonical transformation that clones classical states, we show how this can be implemented by Hamiltonian evolution. We then propose an experiment using the tools of nonlinear optics to realise the ideas presented here. Finally, to understand the cloning process in a more realistic context, we introduce statistical mechanical noise to the system and study how this affects the cloning process. While most of our work deals with linear systems and harmonic oscillators, we give some examples of cloning maps on manifolds and show that any system whose configuration space is a group manifold admits a cloning canonical transformation.