  We consider the 2D alternate quantum walk on a cylinder. We concentrate on
the study of the motion along the open dimension, in the spirit of looking at
the closed coordinate as a small or "hidden" extra dimension. If one starts
from localized initial conditions on the lattice, the dynamics of the quantum
walk that is obtained after tracing out the small dimension shows the
contribution of several components, which can be understood from the study of
the dispersion relations for this problem. In fact, these components originate
from the contribution of the possible values of the quasi-momentum in the
closed dimension. In the continuous space-time limit, the different components
manifest as a set of Dirac equations, with each quasi-momentum providing the
value of the corresponding mass. We briefly discuss the possible link of these
ideas to the simulation of high energy physical theories that include extra
dimensions. Finally, entanglement between the coin and spatial degrees of
freedom is studied, showing that the entanglement entropy clearly overcomes the
value reached with only one spatial dimension.
