We analyze the decoherence in quantum walks in two-dimensional lattices generated by brokenlink-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on 2-D lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the non-symmetric case, when the probability to break links in one direction is different from the probability in the perpendicular direction, we have obtained a non-trivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2-D walk to a coherent 1-D walk.
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