= Bell swapping visibility under random labels
{title2=$v_{\rm out}=v_1v_2q$}
Suppose independent resource pairs have <density matrices> $v_j|\Phi^+\rangle\langle\Phi^+|+(1-v_j)I_4/4$. An ideal complete <Bell-basis measurement>, followed by outcome-dependent <Pauli gates>, produces a chosen <Bell state> with white-noise visibility $v_1v_2$: either white-noise input makes the remote pair maximally mixed. If the reported label is reliable with probability $q$ and otherwise uniformly random, averaging the erroneous corrections makes that branch maximally mixed too, so $v_{\rm out}=v_1v_2q$. A second independent detector of the same quality during <quantum teleportation> adds another factor $q$ to the teleported <Bloch vector>.
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