Robustness of dynamical entropy

Details Robustness of dynamical entropy Robustness of dynamical entropy

2004-11-16

arxiv.org/abs/math-ph/0411055v1

Physics

Mathematical Physics

13 pages

Scientific paper

10.1088/0305-4470/38/10/003

When quantifying the mixing properties of a quantum dynamical system in terms of dynamical entropy, the following scheme appears natural: observe the state of the system at regular time intervals while it evolves and determine the entropy produced over time. It is clear that this entropy will not only depend on the type of dynamics, but also on the type of observations. Intuitively, one can expect that some measurements are better suited than others to reveal information about the dynamics, whereas many will generate undesirable noise. In this paper, we show for two widely used model systems that the dynamical entropy is rather robust in this respect. More precisely, general local positive operator-valued measurements may be restricted to von Neumann type measurements for the shift on a quantum spin chain and gauge-invariant ones for the shift on a Fermion chain.

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