03-48 Igor Bjelakovic, Tyll Kr ger, Rainer Siegmund-Schultze, Arleta Szkola
The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems (278K, .ps.gz) Feb 11, 03
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Abstract. We formulate and prove a quantum Shannon-McMillan theorem. The theorem demonstra tes the significance of the von Neumann entropy for translation invariant ergodic quantum spin systems on $\zz^{\nu}$-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.

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