# LIMIT THEOREMS FOR A LOCALIZATION MODEL OF 2-STATE QUANTUM WALKS

@article{Machida2011LIMITTF, title={LIMIT THEOREMS FOR A LOCALIZATION MODEL OF 2-STATE QUANTUM WALKS}, author={T. Machida}, journal={International Journal of Quantum Information}, year={2011}, volume={09}, pages={863-874} }

We consider 2-state quantum walks (QWs) on the line, which are defined by two matrices. One of the matrices operates the walk at only half-time. In the usual QWs, localization does not occur at all. However, our walk can be localized around the origin. In this paper, we present two limit theorems, that is, one is a stationary distribution and the other is a convergence theorem in distribution.

#### 15 Citations

Limit distribution with a combination of density functions for a 2-state quantum walk

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

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It is shown that typical spatial homogeneous QWs with ballistic spreading belong to the universality class and it is found that the walk treated here with one defect also belongs to the class. Expand

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A QUANTUM WALK WITH A DELOCALIZED INITIAL STATE: CONTRIBUTION FROM A COIN-FLIP OPERATOR

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