= Entanglement-assisted classical capacity
{title2=$C_E(\mathcal N)=\max_\rho I(R;B)$}
This is the supremum of reliable classical bits per use of a <memoryless quantum channel> when sender and receiver share unlimited prior <quantum entanglement>. If $|\psi_\rho\rangle_{RA}$ purifies the input, let $\omega_{RB}=(\operatorname{id}_R\otimes\mathcal N)(|\psi_\rho\rangle\langle\psi_\rho|)$. The single-letter capacity formula is $\max_\rho[S(\rho)+S(\mathcal N(\rho))-S(\omega_{RB})]$, the maximum <quantum mutual information> between reference and output. The preshared resource is independent of the message.
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