A Classical Bound on Quantum Entropy

Abstract

A classical upper bound for quantum entropy is identified and illustrated, $0\le S_q\le \ln (e{\sigma }^2/2\hslash )$, involving the variance ${\sigma }^2$ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.

Latex2e, 7 pages, publication version