= Qubit Pauli twirl
{title2=$\mathcal T(\rho)=I/2$}
For any <qubit> operator $A$,
$$
\mathcal T(A)=\frac14(A+XAX+YAY+ZAZ)=\frac{\operatorname{Tr}A}{2}I.
$$
Expand $A$ in the <Pauli operator> basis. The identity term is fixed, while every nonidentity coefficient has two positive and two negative contributions and cancels. Thus forgetting a uniformly random Pauli key sends every <density operator> to the <maximally mixed state>. This is the dimension-two <Heisenberg-Weyl twirling channel>, since replacing $Y$ by $XZ$ changes only an irrelevant phase in the conjugation.
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