Manuscript Hawk04-A@1 · Hawk04-A.tex · proposition · 526092ba

Proposition: Averaged channels need not decouple realization-wise

What a positive finite-time certificate must contain › Disorder is not averaged away · lines 1748–1763 · proof included or linked

For a qubit, define

C_{0} (ρ) = diag (ρ), C_{1} (ρ) = X diag (ρ) X .

Their equal average is the replacement channel $Tr (ρ) I /2$ , although each realization perfectly distinguishes the logical basis inputs.

Proof. Direct addition gives the average. Each individual pair of basis outputs is orthogonal.

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