  We study the decoherence effects originating from state flipping and
depolarization for two-dimensional discrete-time quantum walks using four-state
and two-state particles. By quantifying the quantum correlations between the
particle and position degree of freedom and between the two spatial ($x-y$)
degrees of freedom using measurement induced disturbance (MID), we show that
the two schemes using a two-state particle are more robust against decoherence
than the Grover walk, which uses a four-state particle. We also show that the
symmetries which hold for two-state quantum walks breakdown for the Grover
walk, adding to the various other advantages of using two-state particles over
four-state particles.
