A Physical Perspective on Classical Cloning

TL;DR

This paper explores how classical states can be cloned physically using Hamiltonian dynamics, proposing an experimental setup with nonlinear optics and analyzing the effects of noise on the process.

Contribution

It introduces a Hamiltonian-based method for classical cloning, including experimental proposals and analysis of noise effects, extending cloning concepts beyond quantum limitations.

Findings

Cloning can be realized via Hamiltonian evolution.

Proposed an experiment using nonlinear optics.

Noise impacts the fidelity of classical cloning.

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.