A limit law of the return probability for a quantum walk on a hexagonal lattice
Abstract
A return probability of random walks is one of the interesting subjects. As it is well known, the return probability strongly depends on the structure of the space where the random walker moves. On the other hand, the return probability of quantum walks, which are quantum models corresponding to random walks, has also been investigated to some extend lately. In this paper, we take care of a discretetime threestate quantum walk on a hexagonal lattice from the view point of mathematics. The mathematical result shows a limit of the return probability when the walker starts off at the origin. The result of the limit tells us about a possibility of localization at the position and a dependence of localization on the initial state.
 Publication:

International Journal of Quantum Information
 Pub Date:
 December 2015
 DOI:
 10.1142/S0219749915500549
 arXiv:
 arXiv:1502.06453
 Bibcode:
 2015IJQI...1350054M
 Keywords:

 Quantum walk;
 hexagonal lattice;
 limit law;
 return probability;
 Quantum Physics;
 Mathematics  Probability
 EPrint:
 9 pages, 3 figures