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The Shannon-McMillan theorem for ergodic quantum lattice systems |
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| Authors: | Igor Bjelakovi Tyll Krüger Rainer Siegmund-Schultze and Arleta Szkoa |
| Institution: | (1) Fakultät II – Mathematik und Naturwissenschaften, Institut für Mathematik MA 7-2, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany;(2) Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33619 Bielefeld, Germany |
| 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   -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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