  We analytically exploit the two-mode Gaussian states nonunitary dynamics. We
show that in the zero temperature limit, entanglement sudden death (ESD) will
always occur for symmetric states (where initial single mode compression is
$z_0$) provided the two mode squeezing $r_0$ satisfies $0 < r_0 < 1/2 \log
(\cosh (2 z_0)).$ We also give the analytical expressions for the time of ESD.
Finally, we show the relation between the single modes initial impurities and
the initial entanglement, where we exhibit that the later is suppressed by the
former.
