The Shannon-McMillan Theorem for AF $C^*$-systems

TL;DR

This paper presents a new proof of the quantum Shannon-McMillan theorem for AF $C^*$-systems, utilizing the variational principle instead of traditional methods, thereby extending its applicability.

Contribution

It introduces a novel proof technique for the quantum Shannon-McMillan theorem tailored to AF $C^*$-systems, expanding the theoretical framework.

Findings

Proof based on the variational principle

Extension of the theorem to AF $C^*$-systems

Provides new insights into quantum information theory

Abstract

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