Entropy and superposition principle

Abstract

Given a faithful normal state ϕ of a von Neumann algebra M, entropy and relative entropy for normal states of M are defined by Radon-Nikodyn derivatives of normal states with respect to ϕ. Most properties of entropy and relative entropy in finite quantum systems are shown to hold. It is also shown that the finiteness of relative entropy is related to the facial superposition principle in quantum theory [5].