Copying quantum states

Abstract

The no-broadcasting theorem in quantum information says that a set of states on a quantum system admits a common broadcasting (copying) operation if and only if their density matrices belong to a commuting family. We discuss and prove this theorem, as well as the closely related “no-cloning theorem” in the context of quantum probability theory, i.e. in the category of (finite dimensional) C*-algebras with unital completely positive maps.