= Controlled-transfer gate
{title2=$c'-d'=\cos\theta(c-d)$}
A controlled <rotation gate> followed by computational-basis <dephasing> mixes the two target populations in the control-one subspace. If they are $c,d$, their sum is preserved and their difference is multiplied by $\cos\theta$. The operation is not unitary after dephasing. On a two-qubit diagonal state, the population of $|00\rangle$ is unchanged when either qubit is the target, because the other control bit is zero.
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