  Linearity of a dynamical entropy means that the dynamical entropy of the
n-fold composition of a dynamical map with itself is equal to n times the
dynamical entropy of the map for every positive integer n. We show that the
quantum dynamical entropy introduced by Slomczynski and Zyczkowski is nonlinear
in the time interval between successive measurements of a quantum dynamical
system. This is in contrast to Kolmogorov-Sinai dynamical entropy for classical
dynamical systems, which is linear in time. We also compute the exact values of
quantum dynamical entropy for the Hadamard walk with varying Luders-von Neumann
instruments and partitions.
