information:classification, quality:corruption
Von Neumann entropy

Von Neumann entropy is extensively used in different forms (conditional entropy, relative entropy, etc.) in the framework of quantum information theory. Entanglement measures are based upon some quantity directly related to the von Neumann entropy. Given a statistical ensemble of quantum mechanical systems with the density matrix ρ {\displaystyle \rho }, it is given by S (ρ) = − Tr (ρ ln ρ). {\displaystyle S(\rho)=-\operatorname {Tr} (\rho \ln \rho).\,} Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as Holevo entropy and conditional quantum entropy. Quantum information theory is largely concerned with the interpretation and uses of von Neumann entropy, a cornerstone in the former's development; the Shannon entropy applies to classical information theory.