Wehrl entropy, entropic uncertainty relations, and entanglement

2021/03/31 by Stefan Floerchinger, Tobias Haas, T. Haas +1 · 37 citations
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Discrete mathematics #Entropic uncertainty #Entropy (arrow of time) #Entropy rate #Joint quantum entropy #Mathematics #Min entropy #Physics #Principle of maximum entropy #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Statistical physics #Statistics #Uncertainty principle #quant-ph

paper · pdf · doi:10.1103/physreva.103.062222

published in Physical Review A 103(6) (American Physical Society) · 15 pages, 3 figures

arxiv created 2021/06/28 · openalex publication_date 2021/06/28 · arxiv updated 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Wehrl entropy is an entropy associated with the Husimi quasiprobability distribution. We discuss how it can be used to formulate entropic uncertainty relations and for a quantification of entanglement in continuous variables. We show that the Wehrl-Lieb inequality is closer to equality than the usual Bia\lynicki-Birula--Mycielski entropic uncertainty relation almost everywhere. Furthermore, we show how Wehrl mutual information can be used to obtain a measurable perfect witness for pure state bipartite entanglement, which additionally provides a lower bound on the entanglement entropy.

Citations

• Inseparability Criteria for Continuous Bipartite Quantum States
• On Information and Sufficiency
• Gaussian quantum information
• Coherent states: Theory and some applications
• A Mathematical Theory of Communication
• Negative Entropy and Information in Quantum Mechanics
• Zur Quantenmechanik einfacher Bewegungstypen
• Entropic Entanglement Criteria for Continuous Variables
• Entanglement Detection: Complexity and Shannon Entropic Criteria
• Information Theory and Statistical Mechanics
• Proof of an entropy conjecture for Bloch coherent spin states and its generalizations
• The Uncertainty Principle
• Wehrl entropy, Lieb conjecture, and entanglement monotones
• "Relative State" Formulation of Quantum Mechanics
• Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams
• Position-momentum uncertainty relations in the presence of quantum memory
• Optimal entanglement witnesses for continuous-variable systems
• �ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
• Inequalities in Fourier Analysis
• Peres-Horodecki Separability Criterion for Continuous Variable Systems
• Entropic uncertainty relations and their applications
• Coherent and Incoherent States of the Radiation Field
• Prior Probabilities
• Gaussian entanglement revisited
• Spatially distributed multipartite entanglement enables EPR steering of atomic clouds
• Exact Shannon entropies for the multidimensional harmonic states
• Quantum Computation and Quantum Information
• Quantum entanglement
• Entanglement detection in quantum many-body systems using entropic uncertainty relations
• On the Quantum Correction For Thermodynamic Equilibrium
• Information Theory and Statistical Mechanics. II

Cited by

• Detecting genuine non-Gaussian entanglement
• Entropic entanglement criteria in phase space