The information entropy of quantum-mechanical states

¹ Department of Physics, Ben-Gurion University - Beer-Sheva 84105, Israel
² Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Paul Sabatier 31062 Toulouse Cedex 4, France
³ Department of Computer Science, Ben-Gurion University - Beer-Sheva 84105, Israel

Received: 19 April 2004
Accepted: 15 June 2004

Abstract

It is well known that a Shannon-based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the von Neumann entropy as the corresponding quantum-mechanical definition. But the latter is problematic from the quantum information point of view. Consequently, we introduce a new definition of entropy that reflects the inherent uncertainty of quantum-mechanical states. We derive for it an explicit expression, and discuss some of its general properties. We distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.