In this paper, we show that a result precisely analogous to the traditional quantum no-cloning theorem holds in classical mechanics. This classical no-cloning theorem does not prohibit classical cloning, we argue, because it is based on a too-restrictive definition of cloning. Using a less popular, more inclusive definition of cloning, we give examples of classical cloning processes. We also prove that a cloning machine must be at least as complicated as the object it is supposed to clone.

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.10.

This proposition remains true even if

*U*is only required to be a linear isometry (see Definition 5).11.

The analogy will be made precise in Sec. IV A.

12.

This proposition remains true even if ϕ is only required to be a symplectic map (see Definition 6).

13.

There appear to be

*two*definitions here, but they are both special cases of a single, more general definition, as explained in Sec. IV A.14.

The propositions that depend on this definition remain true even if

*U*is only required to be a linear isometry (see Definition 5).15.

The propositions that depend on this definition remain true even if ϕ is only required to be a symplectic map (see Definition 6).

16.

The propositions that depend on this definition remain true even if

*U*is only required to be a linear isometry (see Definition 5).17.

The propositions that depend on this definition remain true even if ϕ is only required to be a symplectic map (see Definition 6).

18.

When open systems are taken into consideration, some transformations have to be represented by non-unitary maps, leading to a more complicated categorical setting. One possible choice is the category whose objects and arrows are complex Hilbert spaces and bounded linear maps, discussed in Ref. 2.

© 2012 American Institute of Physics.

2012

American Institute of Physics

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