Decoherence in two-dimensional quantum walks using four- and two-state particles

Abstract

We study the decoherence effects originating from state flipping and depolarization for two-dimensional discrete-time quantum walks using four- and two-state particles. By comparing the quantum correlations between the two spatial (x − y) degrees of freedom using measurement-induced disturbance, 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 break down for the Grover walk, adding to the various other advantages of using two-state rather than four-state particles.