  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. We observe that the spatio-temporal dependence of magnetization
and spin current show the light-cone structure. Moreover, for a fixed site, we
observe specific behaviors which are not seen in the closed XX spin chain. Near
the center of the chain, these quantities exhibit an exponential approach to
the steady state values and the decay time is given by the Liouvillian gap. The
contribution of the corresponding state becomes smaller for sites near a
boundary, where we observe a plateau regime where magnetization does not change
over a duration of time. Using the fact that the time derivative of
magnetization is written as a product of the Bessel function and exponential
function, we can explain various properties of the plateau regime analytically.
