  We discuss the generalized von Neumann (Tsallis) entropy and the generalized
Fisher information (GFI) in nonextensive quantum systems, by using the
interpolation approximation (IA) which has been shown to yield good results for
the quantal distributions within $O(q-1)$ and in high- and low-temperature
limits, $q$ being the entropic index [H. Hasegawa, Phys. Rev. E 80 (2009)
011126]. Three types of GFIs which have been proposed so far in the
nonextensive statistics, are discussed from the viewpoint of their metric
properties and the Cram\'{e}r-Rao theorem. Numerical calculations of the $q$-
and temperature-dependent Tsallis entropy and GFIs are performed for the
electron band model and the Debye phonon model.
