  Consider a discrete-time quantum walk on the $N$-cycle governed by the
following condition: at every time step of the walk, the option persists, with
probability $p$, of exercising a projective measurement on the coin degree of
freedom. For a bipartite quantum system of this kind, we prove that the von
Neumann entropy of the total density operator converges to its maximum value.
Thus, when influenced by decoherence, the mutual information between the two
subsystems, corresponding respectively to the space of the coin and the space
of the walker, eventually must diminish to zero. To put it plainly, any level
of decoherence greater than zero forces the system eventually to become
completely "disentangled".}
