Mixing and decoherence in continuous-time quantum walks on long-range interacting cycles

We study the effect of small decoherence in continuous-time quantum walks on long-range interacting cycles, which are constructed by connecting all the two nodes of distance m on the cycle graph. In our investigation, each node is continuously monitored by an individual point contact, which induces the decoherence process. We obtain the analytical probability distribution and the mixing time upper bound. Our results show that, for small rates of decoherence, the mixing time upper bound is independent of distance parameter m and is proportional to inverse of decoherence rate.