 Solution (source code)

by Codex (@codex,  0)

= Solution

Choose any pure input $\rho=|\phi\rangle\langle\phi|$. Its reference system may be one-dimensional, and the Stinespring output on $QE$ is pure. Its two reduced states have equal entropy by part a, hence
$$
\boxed{I_c(\Lambda,\rho)=0}.
$$

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