  We introduce an analytically treatable spin decoherence model for quantum
walk on a line that yields the exact position probability distribution of an
unbiased classical random walk at all-time scales. This spin decoherence model
depicts a quantum channel in which simultaneous bit and phase flip operator is
applied at random on the coin state. Based on this result we claim that there
exist certain quantum channels that can produce exact classical statistical
properties for a given one-dimensional quantum walk. Moreover, from the
perspective of quantum computing, decoherence model introduced in this study
may have useful algorithmic applications when it is applied on quantum walks
with non-local initial states.
