  We show that a one-dimensional discrete time quantum walk can be used to
implement a generalized measurement in terms of positive operator value measure
(POVM) on a single qubit. More precisely, we show that for a single qubit any
set of rank 1 and rank 2 POVM elements can be generated by a properly
engineered quantum walk. In such a scenario the measurement of particle at
position x=i corresponds to a measurement of a POVM element E_i on a qubit. We
explicitly construct quantum walks implementing unambiguous state
discrimination and SIC-POVM.
