= Entanglement-assisted capacity of a quantum erasure channel
{title2=$C_E(\mathcal E_p)=2(1-p)\log_2 D$}
For input dimension $D$, an input of entropy $S(\rho)$ gives output entropy $h_2(p)+(1-p)S(\rho)$ and reference-output entropy $h_2(p)+pS(\rho)$. These follow from <entropy of an orthogonal quantum mixture> and purity of the input purification. Thus the <quantum mutual information> is $2(1-p)S(\rho)$, maximized at $\rho=I_D/D$. The <entanglement-assisted classical capacity> is consequently $2(1-p)\log_2D$ bits per use; for a binary input it is $2(1-p)$.
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