The Shannon-McMillan Theorem for AF $C^{\ast }$-systems

Abstract

We give a new proof of quantum Shannon-McMillan theorem, extending it to AF $C^{\ast }$-systems. Our proof is based on the variational principle, instead of the classical Shannon-McMillan theorem.

References in corpus (4)

• An Ergodic Theorem for the Quantum Relative Entropy
• Quantum Macrostates, Equivalence of Ensembles and an H-Theorem
• Quantum sources and a quantum coding theorem
• The McMillan theorem for a class of asymptotically abelian C*-algebras

Cited by in corpus (2)

• Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
• Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma