Lower Bound for Entanglement-Assisted Classical Communication in Asymptotic Setting

Let $\mathcal{N}$ be a quantum channel. Let $I$ denote the channel mutual information functional and let $C$ denote entanglement-assisted classical capacity. The channel mutual information $I(\mathcal{N})$ is an achievable entanglement-assisted classical communication rate. Consequently, \[ C_{\operatorname{EA}}(\mathcal{N}) \ge I(\mathcal{N}). \]