  Hilbert - Schmidt and trace norm geometric quantum discord are compared with
regard to their behavior during local time evolution. We consider the system of
independent two - level atoms with time evolution given by the dissipative
process of spontaneous emission. It is explicitly shown that the Hilbert -
Schmidt norm discord has nonphysical properties with respect to such local
evolution and cannot serve as a reasonable measure of quantum correlations and
the better choice is to use trace norm discord as such a measure.
