  The quantum random walk has been much studied recently, largely due to its
highly nonclassical behavior. In this paper, we study one possible route to
classical behavior for the discrete quantum walk on the line: the presence of
decoherence in the quantum ``coin'' which drives the walk. We find exact
analytical expressions for the time dependence of the first two moments of
position, and show that in the long-time limit the variance grows linearly with
time, unlike the unitary walk. We compare this to the results of direct
numerical simulation, and see how the form of the position distribution changes
from the unitary to the usual classical result as we increase the strength of
the decoherence.
