= Holevo-capacity additivity for entanglement-breaking channels
{c}
{title2=$\chi^*(\mathcal E\otimes\mathcal N)=\chi^*(\mathcal E)+\chi^*(\mathcal N)$}
Every <entanglement-breaking channel> $\mathcal E$ has additive <Holevo capacity> with every finite-dimensional <quantum channel> $\mathcal N$. A <measure-and-prepare channel> factorization exposes a classical measurement outcome. The <quantum mutual information balance identity> and <data processing for quantum mutual information> then bound the joint output <Holevo quantity> by the sum of the individual capacities, using the <conditional input ensemble after a local measurement> for the other channel. Independent product ensembles attain the reverse inequality.
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