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We give a new proof of quantum Shannon-McMillan theorem, extending it to AF $C^*$-systems.
C. Shannon: A mathematical theory of communication
1948
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O. Bratteli, D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics 1
1986
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F. Hiai, D. Petz: The proper formula for relative entropy and its asymptotics in quantum probability
1991
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O. Bratteli, D. W. Robinson: Operator Algebras and Quantum Statistical Mechanics 2
1996
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F. Hiai, D. Petz: Quantum Mechanics in AF C ∗ C^{*} -systems
1996
Cited alongside, same era.
V. Y. Golodets, S. Neshveyev: Gibbs states for AF algebras
1998
Cited alongside, same era.
I. Bjelaković, T. Krüger, R. Siegmund-Schultze, A. Szkola: The Shannon-McMillan theorem for ergodic quantum lattice systems
2004
Cited alongside, same era.
S. Neshveyev, E. Størmer: The McMillan theorem for a class of asymptotically abelian C ∗ C^{*} -algebras
Cited in the paper.
I. Bjelaković, R. Siegmund-Schultze: An ergodic theorem for the quantum relative entropy
2004
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D. Ruelle : Thermodynamic formalism
2004
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S. Neshveyev, E. Størmer: Dynamical entropy in operator algebras
2006
Later among the works it cites.
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