The information entropy of quantum-mechanical states

Abstract

It is well known that a Shannon-based definition of informationentropy leads in the classical case to the Boltzmann entropy. Itis tempting to regard the von Neumann entropy as the correspondingquantum-mechanical definition. But the latter is problematic fromthe quantum information point of view. Consequently, we introducea new definition of entropy that reflects the inherent uncertaintyof quantum-mechanical states. We derive for it an explicitexpression, and discuss some of its general properties. Wedistinguish between the minimum uncertainty entropy of purestates, and the excess statistical entropy of mixtures.