The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems
<|reference_start|>The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems: 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.<|reference_end|>
@article{bjelakovic2002the,
    title={The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems},
    author={Igor Bjelakovic, Tyll Krueger, Rainer Siegmund-Schultze, Arleta Szkola},
    journal={arXiv preprint arXiv:math/0207121},
    year={2002},
    archivePrefix={arXiv},
    eprint={math/0207121},
    primaryClass={math.DS cs.DS cs.IT math-ph math.IT math.MP math.OA quant-ph}
}