Solution
= Solution
For an <anti-degradable quantum channel>, a channel from $E$ simulates $Q$. The <data-processing inequality for quantum relative entropy> applied to <quantum mutual information> gives $I(R:Q)\leq I(R:E)$. Part d then implies $I_c(\Lambda,\rho)\leq0$ for every input. Part c supplies a pure input attaining zero, so
$$
\boxed{Q^{(1)}(\Lambda)=\max_\rho I_c(\Lambda,\rho)=0}.
$$