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Defining quantum dynamical entropy


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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Alicki, R., Fannes, M. Defining quantum dynamical entropy. Lett Math Phys 32, 75–82 (1994).

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Mathematics Subject Classifications (1991)

  • 46L55
  • 28D20
  • 82B10