 Holevo's theorem

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.

Holevo's theorem is a fundamental result in quantum information theory that provides a limit to the amount of classical information that can be extracted from a quantum system. Specifically, it relates to the transmission of classical information through quantum states and deals with how much information can be extracted from measurements on a quantum ensemble.