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A physical perspective on classical cloning. (English) Zbl 1476.81022

Summary: 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.

MSC:

81P50 Quantum state estimation, approximate cloning
70H05 Hamilton’s equations
70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
78A60 Lasers, masers, optical bistability, nonlinear optics
60H50 Regularization by noise
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