Abstract
Wildberger introduced the method of constructing a Hermitian discrete hypergroup from a random walk on a graph. In this study, we will apply his method to an open quantum random walk (OQRW) on a distance set and show that any discrete hypergroup that is not necessarily Hermitian can be realized using the OQRW on a distance set. We also investigate the distributions of OQRWs on distance sets in the view point of hypergroups.
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