# Can all kinds of pure non-entangled states be cloned?

Is it correct to say that for an $$n$$-qubit system, we can clone all kinds of pure non-entangled states, without violating the no-cloning theorem?

That is, is the correct interpretation for the proof of cloning theorem shown here, to be that if such a cloning operator $$U$$ exists, such an operator $$U$$ would not be a linear operator, but nonetheless $$U$$ can still act on only non-entangled, mutually orthogonal states?

Entangled linear superpositions of those states in the set are not included instead, because then $$U$$ would not be a linear operator.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
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Sep 8, 2021 at 15:47
• Hi 王天羿, I have tried editing your post for readability. Please let me know if this is the spirit of your question! Sep 8, 2021 at 21:55
• @MarkS Yep! Thanks! Sep 9, 2021 at 2:31
• @Community Hi, is my question ready to be open to answer? Sep 9, 2021 at 3:19
• I don't think entanglement is important for no-cloning. Even with a single qubit and only pure states you have the no-cloning theorem. Sep 9, 2021 at 7:04