Manuscript X-K-ST@1 · X-K-ST.tex · proposition · 93c39c0f

Proposition: Calibration on one state is not a channel bound

Complete-channel and state-specific error bounds › Two explicit error pitfalls · lines 1338–1349 · proof included or linked

X-K-ST@1#prop:stateversusdiamond

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Two channels can agree exactly on one tested state and have half-diamond distance one.

Proof. On a qubit, $id$ and $Ad_{Z}$ agree on $∣ 0 ⟩ ⟨ 0 ∣$ . Their outputs on $∣ + ⟩ ⟨ + ∣$ are $∣ + ⟩ ⟨ + ∣$ and $∣ - ⟩ ⟨ - ∣$ , which are orthogonal. Thus their half-diamond distance is one.

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section: Two explicit error pitfalls