A Classical Bound on Quantum Entropy

TL;DR

This paper establishes a classical upper bound on quantum entropy based on phase space variance, providing insights into quantum information limits and extending to Renyi entropy generalizations.

Contribution

It introduces a classical upper bound for quantum entropy involving phase space variance, connecting classical and quantum information measures.

Findings

Quantum entropy is bounded above by a function of phase space variance.

The bound applies to Renyi entropy generalizations.

Illustrations demonstrate the bound's applicability.

Abstract

A classical upper bound for quantum entropy is identified and illustrated, $0\leq S_q \leq \ln (e \sigma^2 / 2\hbar)$, 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.