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

Exact solution for the Lindbladian dynamics for the open XX spin chain with boundary dissipation