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Defining quantum dynamical entropy

Letters in Mathematical Physics volume 32, pages 75–82 (1994)Cite this article

Abstract

We propose an elementary definition of the dynamical entropy for a discrete-time quantum dynamical system. We apply our construction to classical dynamical systems and to the shift on a quantum spin chain. In the first case, we recover the Kolmogorov-Sinai invariant and, for the second, we find the mean entropy of the invariant state plus the logarithm of the dimension of the single-spin space.

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Author notes

  1. R. Alicki

    Present address: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, PL-80-952, Gdańsk, Poland

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Leuven, B-3001, Heverlee, Belgium

    R. Alicki & M. Fannes

Authors
  1. R. Alicki
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  2. M. Fannes
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Alicki, R., Fannes, M. Defining quantum dynamical entropy. Lett Math Phys 32, 75–82 (1994). https://doi.org/10.1007/BF00761125

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  • DOI: https://doi.org/10.1007/BF00761125

Mathematics Subject Classifications (1991)

  • 46L55
  • 28D20
  • 82B10