The Shannon-McMillan theorem for AF \(C^\ast\)-systems

DOI10.1007/s11005-013-0647-0zbMath1286.46072arXiv1303.2288OpenAlexW1973232125MaRDI QIDQ381016

Yoshiko Ogata

Publication date: 15 November 2013

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2288

zbMATH Keywords

variational principlequantum Shannon-McMillan theorem

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55)

Related Items (1)

Asymptotic reversibility of thermal operations for interacting quantum spin systems via generalized quantum Stein’s lemma

Cites Work

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• A Mathematical Theory of Communication
• The proper formula for relative entropy and its asymptotics in quantum probability
• The Shannon-McMillan theorem for ergodic quantum lattice systems
• An ergodic theorem for the quantum relative entropy
• Quantum macrostates, equivalence of ensembles, and an H-theorem
• Quantum sources and a quantum coding theorem
• QUANTUM MECHANICS IN AFC*-SYSTEMS
• Gibbs states for AF algebras
• Thermodynamic Formalism
• Dynamical Entropy in Operator Algebras
• Relatively prime numbers and invariant measures under the natural action of SL (n, \mathbb{Z}) on \mathbb{R}^{n}

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