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Defining quantum dynamical entropy. (English) Zbl 0814.46055
Summary: 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.

MSC:
46L55 Noncommutative dynamical systems
28D20 Entropy and other invariants
82B10 Quantum equilibrium statistical mechanics (general)
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