The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems
Dynamical Systems
2007-07-16 v3 Data Structures and Algorithms
Information Theory
Mathematical Physics
math.IT
math.MP
Operator Algebras
Quantum Physics
Abstract
We formulate and prove a quantum Shannon-McMillan theorem. The theorem demonstrates the significance of the von Neumann entropy for translation invariant ergodic quantum spin systems on n-dimensional lattices: the entropy gives the logarithm of the essential number of eigenvectors of the system on large boxes. The one-dimensional case covers quantum information sources and is basic for coding theorems.
Cite
@article{arxiv.math/0207121,
title = {The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems},
author = {Igor Bjelakovic and Tyll Krueger and Rainer Siegmund-Schultze and Arleta Szkola},
journal= {arXiv preprint arXiv:math/0207121},
year = {2007}
}
Comments
21 pages, extended version concerning subalgebras