  We present two long-time limit theorems of a 3-state quantum walk on the line
when the walker starts from the origin. One is a limit measure which is
obtained from the probability distribution of the walk at a long-time limit,
and the other is a convergence in distribution for the walker's position in a
rescaled space by time. In addition, as an application of the walk, we obtain
discrete uniform limit measures from the 3-state walk with a delocalized
initial state.
