Rainer Siegmund-Schultze

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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 Z ν-lattices: the en-tropy gives the logarithm of the essential number of eigenvectors of the system on large boxes. The one-dimensional case covers quantum information(More)
In classical information theory, entropy rate and algorithmic complexity per symbol are related by a theorem of Brudno. In this paper , we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity , both based on the shortest qubit descriptions of qubit strings that, run by a universal(More)
We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to(More)
—We define an algorithm that parses multidimen-sional arrays sequentially into mainly unrepeated but nested multidimensional sub-arrays of increasing size, and show that the resulting sub-block pointer encoder compresses almost every realization of any finite-alphabet ergodic process on Z d ≥0 to the entropy, in the limit.
  • J.-C N Abarenkova, S Angì Es D Auriac, J.-M Bourkraa, Maillard, Growth-Complexity, A R L G Adler +41 others
  • 2008
30. A. Hone. Diophantine nonintegrability of a third order recurrence with the Laurent property. two discrete integrability criteria: singularity confinement and algebraic entropy. (87j:05003) 45. T. Takenawa. A geometric approach to singularity confinement and algebraic entropy. Algebraic entropy and the space of initial values for discrete dynamical(More)
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