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Numerous papers on quantum cloning have been written since 1996, including both theoretical and experimentally focused papers. The following survey paper is a good place to start if you want to learn more: Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acin. Quantum cloning. Reviews of Modern Physics 77: 1225-1256, 2005. arXiv:quant-ph/...

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Regarding the optimality of the results of your linked article [1],$\def\ket#1{\lvert#1\rangle}\def\bra#1{\!\langle#1\rvert}$ we find in Section III A that on input $\ket{\phi}$, the states produced by this imperfect cloning operation are of the form \qquad\qquad\qquad \rho_{\text{out}} \,=\, \tfrac{5}{6}\ket{\phi}\bra{\phi} \,+\, \tfrac{1}{6}\... 9 To simplify the question consider CNOT gate instead of Toffoli gate; CNOT is also fanout because \begin{align} |0\rangle|0\rangle \rightarrow |0\rangle|0\rangle\\ |1\rangle|0\rangle \rightarrow |1\rangle|1\rangle \end{align} and it looks like cloning for any basis state x\in\{0,1\} \begin{align} |x\rangle|0\rangle \rightarrow |x\rangle|x\rangle \end{... 5 As John Watrous said, the Rev. Mod. Phys. article is an excellent starting point. If you want to know the sort of thing that's been looked at since, then in a shameless bit of self-promotion, you might look at this paper. There have been a couple of follow-up papers as well (including one that closes a small step left open in one of the proofs). What is ... 4 Assume this works. Then, nothing prevents Alice from applying the same protocol to a quantum state that is known to her, such as |0\rangle or |1\rangle. This way, she could send information to Bob instantaneously. Thus, it violates faster-than-light communication and thus is impossible. 3 You may also want to check for: state dependent deterministic cloners which clone with a better fidelity when input state comes from a known ensemble. Ref: Bruss et al., PRA 57, 2368 (1997) probabilistic cloners which clone with unit fidelity but with less than unity success probability asymmetric cloners where the outputs have cloned with different ... 3 The no-cloning theorem states that an unknown quantum state cannot be copied exactly --- so this rules out any algorithm that attempts to produce perfect copies of an arbitrary quantum state (including squeezed and coherent states). As you note, however, the no-cloning theorem does not rule out the production of approximate quantum state clones. Andersen et ... 2 You seem to be mixing two very different concepts here. Quantum cloning is talking about the absolute limits of what is theoretically possible in a perfect world. In this absolute theoretical limit, yes we can derive how well quantum cloning can work, and we also know that classical cloning is nominally perfect. There is then a separate question of how well ... 2 The no cloning theorem says that there is no circuit which creates independent copies of all quantum states. Mathematically, no cloning states that:\forall C: \exists a,b: C \cdot \Big( (a|0\rangle + b|1\rangle)\otimes|0\rangle \Big) \neq (a|0\rangle + b|1\rangle) \otimes (a|0\rangle + b|1\rangle) Fanout circuits don't violate this theorem. They don't ...

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