Manuscript Hawk07-A@1 · Hawk07-A.tex · proposition · f9c0f5da

Proposition: No-cloning channel form

No duplicate logical exterior · lines 1621–1635 · proof included or linked

No CPTP map clones every pure state of a nontrivial diary.

Proof. Dilate a proposed cloner. Pure clone marginals force

W ∣ ψ ⟩ = ∣ ψ ⟩ ∣ ψ ⟩ ∣ χ_{ψ} ⟩ .

For two input states with overlap modulus $0 < c < 1$ , isometry gives

c = c^{2} ∣ ⟨ χ_{ϕ} ∣ χ_{ψ} ⟩ ∣ \leq c^{2},

a contradiction.

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