# Limit theorems of a two-phase quantum walk with one defect

@article{Endo2015LimitTO, title={Limit theorems of a two-phase quantum walk with one defect}, author={Shimpei Endo and T. Endo and N. Konno and M. Takei and E. Segawa}, journal={Quantum Inf. Comput.}, year={2015}, volume={15}, pages={1373-1396} }

We treat a position dependent quantum walk (QW) on the line which we assign two different time-evolution operators to positive and negative parts respectively. We call the model "the two-phase QW" here, which has been expected to be a mathematical model of the topological insulator. We obtain the stationary and time-averaged limit measures related to localization for the two-phase QW with one defect. This is the first result on localization for the two-phase QW. The analytical methods are… CONTINUE READING

21 Citations

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 29 REFERENCES

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

- Computer Science, Physics
- 2013

66

Localization and fractality in inhomogeneous quantum walks with self-duality.

- Physics, Mathematics
- 2010

73

Continuous-time quantum walks on semi-regular spidernet graphs via quantum probability theory

- Physics, Mathematics
- 2010

22