  We consider the limit distributions of open quantum random walks on
one-dimensional lattice space. We introduce a dual process to the original
quantum walk process, which is quite similar to the relation of
Schr\"odinger-Heisenberg representation in quantum mechanics. By this, we can
compute the distribution of the open quantum random walks concretely for many
examples and thereby we can also obtain the limit distributions of them. In
particular, it is possible to get rid of the initial state when we consider the
evolution of the walk, it appears only in the last step of the computation.
