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Sfb288 logo Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 579


The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems

Igor Bjelakovic, Tyll Krüger, Rainer Siegmund-Schultze, Arleta Szkola

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 $zz^{ u}$-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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