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The Shannon-McMillan Theorem for Ergodic Quantum Lattice Systems | | Igor Bjelakovic
; Tyll Krueger
; Rainer Siegmund-Schultze
; Arleta Szkola
; | | Date: |
15 Jul 2002 | | Subject: | Dynamical Systems; Mathematical Physics; Operator Algebras; Data Structures and Algorithms; Information Theory MSC-class: 46L89; 68P30; 81Qxx | math.DS cs.DS cs.IT math-ph math.MP math.OA quant-ph | | 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 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. | | Source: | arXiv, math.DS/0207121 | | Services: | Forum | Review | PDF | Favorites | |
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