Holevo bound

The Holevo bound is a fundamental theorem in quantum information theory that limits how much classical information can be extracted from a quantum state. Named after Alexander Holevo, it proves that the mutual information between a classical message and the outcome of a quantum measurement is bounded by the von Neumann entropy of the ensemble of quantum states used to encode the message. This bound is tight: there exist encoding and measurement schemes that achieve it, but no scheme can exceed it.

The Holevo bound is the quantum analogue of the classical data processing inequality, but it is strictly stronger. In classical information theory, measuring a signal does not destroy it; in quantum information theory, measurement collapses the state, and the Holevo bound captures the irreversible loss of information that results. It is one of the central results that makes quantum communication fundamentally different from classical communication.