  We investigate the evolution of a discrete-time one-dimensional quantum walk
driven by a position-dependent coin. The rotation angle which depends upon the
position of a quantum particle parameterizes the coin operator. For different
values of the rotation angle, we observe that such a coin leads to a variety of
probability distributions, e.g. localized, periodic, classical-like,
semi-classical-like, and quantum-like. Further, we study the Shannon entropy
associated with position space and coin space of a quantum particle and compare
it with the case of the position-independent coin. We show that the entropy is
smaller for most values of the rotation angle as compared to the case of the
position-independent coin. We also study the effect of entanglement on the
behavior of probability distribution and Shannon entropy of a quantum walk by
considering two identical position-dependent entangled coins. We observe that
in general, a quantum particle becomes more localized as compared to the case
of the position-independent coin and hence the corresponding Shannon entropy is
minimum. Our results show that position-dependent coin can be used as a
controlling tool of quantum walks.
