Holevo quantity ($\chi$)

For an ensemble $\{p_x,{\rho }_x\}$ with average $\bar{\rho }$, the Holevo quantity is $\chi =S(\bar{\rho })-{\sum }_x{p}_{x}S({\rho }_x)=I(X:B)$ of the associated classical-quantum state.

The classical mutual information obtained by any measurement of a quantum ensemble is at most its Holevo quantity. This follows from the data-processing inequality for quantum relative entropy applied to the measurement channel.