A classical bound on quantum entropy

2006/09/30 by Cosmas Zachos, Cosmas K Zachos · 2 citations
Mathematics · Physics and Astronomy · #Classical capacity #Classical limit #Entropy (arrow of time) #Generalized relative entropy #Joint quantum entropy #Mathematical analysis #Mathematical physics #Mathematics #Open quantum system #Phase space #Physics #Principle of maximum entropy #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum channel #Quantum chaos and dynamical systems #Quantum discord #Quantum information #Quantum mechanics #Quantum relative entropy #Rényi entropy #Statistical Mechanics and Entropy #Statistical physics #Statistics #Upper and lower bounds #gr-qc #hep-th #physics.comp-ph #quant-ph

paper · pdf · doi:10.1088/1751-8113/40/21/f02

published as J.Phys.A40:F407-F412,2007 · Latex2e, 7 pages, publication version

arxiv created 2007/04/23 · openalex publication_date 2007/05/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A classical upper bound for quantum entropy is identified and illustrated, 0\≤ S_q \≤ \ln (e \σ² / 2\ℏ), involving the variance \σ² 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.

Citations

• A Mathematical Theory of Communication
• Moments of the Wigner function and Renyi entropies at freeze-out
• On the principles of elementary quantum mechanics
• Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems
• Observability of Rényi’s entropy
• A comment on quantum distribution functions and the OSV conjecture

Cited by

• Quantum corrections to the entropy in a driven quantum Brownian motion model
• Rényi entropy [wikipedia]