  We advance the previous studies of quantum walks on the line with two coins.
Such four-state quantum walks driven by a three-direction shift operator may
have nonzero stationary distributions (localization), thus distinguishing
themselves from the quantum walks on the line in the basic scenario (i.e.,
driven by a single coin). In this work, asymptotic position distributions of
the quantum walks are examined. We derive a weak limit for the quantum walks
and explicit formulas of stationary probability distribution, whose
dependencies on the coin parameter and the initial state of quantum walks are
presented. In particular, it is shown that the weak limit for the present
quantum walks can be of the form in the basic scenario of quantum walks on the
line, for certain initial states of the walk and certain values of the coin
parameter. In the case where localization occurs, we show that the stationary
probability exponentially decays with the absolute value of a walker's
position, independent of the parity of time.
