= Solution
{c}
Use the unnormalized <Choi matrix> convention $J_r=\sum_{j,k=0}^1|j\rangle\langle k|\otimes\mathcal E_r(|j\rangle\langle k|)$, which has trace two. In the ordered basis $|00\rangle,|01\rangle,|10\rangle,|11\rangle$,
$$
\boxed{J_r=\frac12\begin{pmatrix}
1+r&0&0&2r\\
0&1-r&0&0\\
0&0&1-r&0\\
2r&0&0&1+r
\end{pmatrix}.}
$$
Equivalently $J_r=2r|\Omega\rangle\langle\Omega|+(1-r)I_4/2$. The convention obtained by applying the channel to one half of the normalized Bell state gives $J_r/2$; its positivity criterion is the same.
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