  We investigate the global chirality distribution of the quantum walk on the
line when decoherence is introduced either through simultaneous measurements of
the chirality and particle position, or as a result of broken links. The first
mechanism drives the system towards a classical diffusive behavior. This is
used to build new quantum games, similar to the spin-flip game. The second
mechanism involves two different possibilities: (a) All the quantum walk links
have the same probability of being broken. (b) Only the quantum walk links on a
half-line are affected by random breakage. In case (a) the decoherence drives
the system to a classical Markov process, whose master equation is equivalent
to the dynamical equation of the quantum density matrix. This is not the case
in (b) where the asymptotic global chirality distribution unexpectedly
maintains some dependence with the initial condition. Explicit analytical
equations are obtained for all cases.
