  The time evolution of one- and two-dimensional discrete-time quantum walk
with increase in disorder is studied. We use spatial, temporal and
spatio-temporal broken periodicity of the unitary evolution as disorder to
mimic the effect of disordered/random medium in our study. Disorder induces a
dramatic change in the interference pattern leading to localization of the
quantum walks in one- and two-dimensions. Spatial disorder results in the
decreases of the particle and position entanglement in one-dimension and
counter intuitively, an enhancement in entanglement with temporal and
spatio-temporal disorder is seen. The study signifies that the Anderson
localization of quantum state without compromising on the degree of
entanglement could be implement in a large variety of physical settings where
quantum walks has been realized. The study presented here could make it
feasible to explore, theoretically and experimentally the interplay between
disorder and entanglement. This also brings up a variety of intriguing
questions relating to the negative and positive implications on algorithmic and
other applications.
