Cloning in nonlinear Hamiltonian quantum and hybrid mechanics

TL;DR

This paper investigates the possibility of state cloning in nonlinear Hamiltonian quantum and hybrid mechanics, revealing conditions under which cloning is possible or impossible in these generalized frameworks.

Contribution

It demonstrates that nonlinear Hamiltonian quantum mechanics can allow cloning with a machine, while mean-field hybrid mechanics cannot, highlighting fundamental differences.

Findings

Nonlinear Hamiltonian quantum mechanics permits cloning with a machine.

Mean-field hybrid mechanics does not allow cloning by natural evolution.

Hybrid mechanics can enable superluminal communication without cloning.

Abstract

Possibility of state cloning is analyzed in two types of generalizations of quantum mechanics with nonlinear evolution. It is first shown that nonlinear Hamiltonian quantum mechanics does not admit cloning without the cloning machine. It is then demonstrated that the addition of the cloning machine, treated as a quantum or as a classical system, makes the cloning possible by nonlinear Hamiltonian evolution. However, a special type of quantum-classical theory, known as the mean-field Hamiltonian hybrid mechanics, does not admit cloning by natural evolution. The latter represents an example of a theory where it appears to be possible to communicate between two quantum systems at super-luminal speed, but at the same time it is impossible to clone quantum pure states.