  We analyze the quantum walk on a cycle using discrete Wigner functions as a
way to represent the states and the evolution of the walker. The method
provides some insight on the nature of the interference effects that make
quantum and classical walks different. We also study the behavior of the system
when the quantum coin carried by the walker interacts with an environment. We
show that for this system quantum coherence is robust for initially delocalized
states of the walker. The use of phase-space representation enables us to
develop an intuitive description of the nature of the decoherence process in
this system.
