Igor Bjelakovic, Tyll Kr ger, Rainer Siegmund-Schultze, Arleta Szkola
The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems
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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.