Holevo quantity under a quantum channel ($\chi (\{p_x,\Lambda ({\rho }_x)\})\le \chi (\{p_x,{\rho }_x\})$)

Attach an orthogonal classical label register to an ensemble. Its quantum mutual information with the quantum system equals the ensemble Holevo quantity. A local quantum channel changes the ensemble states but preserves their labels and probabilities. Data processing for quantum mutual information then proves that the output Holevo quantity cannot exceed the input value.