# 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} }

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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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 22 REFERENCES

Limit measures of inhomogeneous discrete-time quantum walks in one dimension

- Computer Science, Physics
- 2013

66

Limit theorems for the discrete-time quantum walk on a graph with joined half lines

- Mathematics, Physics
- 2012

12