Proof of an entropy conjecture for Bloch coherent spin states and its generalizations

DOI10.1007/s11511-014-0113-6zbMath1298.81116arXiv1208.3632OpenAlexW3103064417WikidataQ59255689 ScholiaQ59255689MaRDI QIDQ2015964

Jan Philip Solovej, Elliott H. Lieb

Publication date: 18 June 2014

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3632

zbMATH Keywords

entropyminimizerquantum channelcoherent state

Mathematics Subject Classification ID

Cryptography (94A60) Coherent states (81R30) Channel models (including quantum) in information and communication theory (94A40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum communication in Rindler spacetime
• The classical limit of quantum partition functions
• On the relation between classical and quantum-mechanical entropy
• Some integral identities and inequalities for entire functions and their application to the coherent state transform
• Quantum coherent operators: A generalization of coherent states
• Proof of an entropy conjecture of Wehrl
• A lower bound for the Wehrl entropy of quantum spin with sharp high-spin asymptotics
• On Lieb's conjecture for the Wehrl entropy of Bloch coherent states
• The classical limit of quantum spin systems
• The Stability of Matter in Quantum Mechanics
• Proof of the generalized Lieb-Wehrl conjecture for integer indices larger than one
• A simple proof of Wehrl's conjecture on entropy
• An Infinite Sequence of Additive Channels: The Classical Capacity of Cloning Channels

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