We look at two possible routes to classical behavior for the discrete quantum
random walk on the line: decoherence in the quantum ``coin'' which drives the
walk, or the use of higher-dimensional coins to dilute the effects of
interference. We use the position variance as an indicator of classical
behavior, and find analytical expressions for this in the long-time limit; we
see that the multicoin walk retains the ``quantum'' quadratic growth of the
variance except in the limit of a new coin for every step, while the walk with
decoherence exhibits ``classical'' linear growth of the variance even for weak
decoherence.Comment: 4 pages RevTeX 4.0 + 2 figures (encapsulated Postscript). Trimmed for
length. Minor corrections + one new referenc