  We study a spin-1/2-particle moving on a one dimensional lattice subject to
disorder induced by a random, space-dependent quantum coin. The discrete time
evolution is given by a family of random unitary quantum walk operators, where
the shift operation is assumed to be deterministic. Each coin is an independent
identically distributed random variable with values in the group of two
dimensional unitary matrices. We derive sufficient conditions on the
probability distribution of the coins such that the system exhibits dynamical
localization. Put differently, the tunneling probability between two lattice
sites decays rapidly for almost all choices of random coins and after arbitrary
many time steps with increasing distance. Our findings imply that this effect
takes place if the coin is chosen at random from the Haar measure, or some
measure continuous with respect to it, but also for a class of discrete
probability measures which support consists of two coins, one of them being the
Hadamard coin.
