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We study the relations between the averaged linear entropy production inperiodically measured quantum systems and ergodic properties of their classicalcounterparts. Quantized linear automorphisms of the torus, both classicallychaotic and regular ones, are used as examples. Numerical calculations showdifferent entropy production regimes depending on the relation between theKolmogorov-Sinai entropy and the measurement entropy. The hypothesis of freeindependence relations between the dynamics and measurement proposed to explainthe initial constant and maximal entropy production is tested numerically forthose models.Comment: 7 pages, 5 figure

Linear dynamical entropy and free-independence for quantized linear maps on the torus