Localization of quantum walks induced by recurrence properties of random walks

@article{Segawa2011LocalizationOQ,
  title={Localization of quantum walks induced by recurrence properties of random walks},
  author={E. Segawa},
  journal={arXiv: Quantum Physics},
  year={2011}
}
  • E. Segawa
  • Published 2011
  • Mathematics, Physics
  • arXiv: Quantum Physics
  • We study a quantum walk (QW) whose time evolution is induced by a random walk (RW) first introduced by Szegedy (2004). We focus on a relation between recurrent properties of the RW and localization of the corresponding QW. We find the following two fundamental derivations of localization of the QW. The first one is the set of all the $\ell^2$ summable eigenvectors of the corresponding RW. The second one is the orthogonal complement, whose eigenvalues are $\pm 1$, of the subspace induced by the… CONTINUE READING

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