= Solution
A <unital quantum channel> preserves the identity operator: $\Phi(I)=I$. For equal input and output dimensions, this is equivalent to preserving the maximally mixed <density operator>.
For the <amplitude damping channel>,
$$
\Phi(I)=A_0A_0^\dagger+A_1A_1^\dagger
=\begin{pmatrix}1+p&0\\0&1-p\end{pmatrix}.
$$
Thus \b[the channel is not unital for $p>0$; it is unital only at $p=0$, when it is the identity channel.] In particular, it biases the <maximally mixed state> toward the atomic ground state. The trace-preservation condition involves $\sum_jA_j^\dagger A_j$, whereas unitality involves the opposite products $\sum_jA_jA_j^\dagger$.
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