Spontaneous emission and quantum discord: Comparison of Hilbert-Schmidt and trace distance discord

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.