  We obtain exact formulas for the time-dependence of a few physical
observables for the open XX spin chain with Lindbladian dynamics. Our analysis
is based on the fact that the Lindblad equation for an arbitrary open quadratic
system of $N$ fermions is explicitly solved in terms of diagonalization of a
$4N\times4N$ matrix called structure matrix by following the scheme of the
third quantization. We mainly focus on the time-dependence of magnetization and
spin current. As a short-time behavior at a given site, we observe the plateau
regime except near the center of the chain. Basic features of this are
explained by the light-cone structure created by propagations of boundary
effects from the initial time, but we can explain their more detailed
properties analytically using our exact formulas. On the other hand, after the
plateau regime, the magnetization and spin current exhibit a slow decay to the
steady state values described by the Liouvillian gap. We analytically establish
its $O(N^{-3})$ scaling and also determine its coefficient.
