Localization and limit laws of a threestate alternate quantum walk on a twodimensional lattice
Abstract
A twodimensional discretetime quantum walk (DTQW) can be realized by alternating a twostate DTQW in one spatial dimension followed by an evolution in the other dimension. This was shown to reproduce a probability distribution for a certain configuration of a fourstate DTQW on a twodimensional lattice. In this work we present a threestate alternate DTQW with a parametrized coinflip operator and show that it can produce localization that is also observed for a certain other configuration of the fourstate DTQW and nonreproducible using the twostate alternate DTQW. We will present two limit theorems for the threestate alternate DTQW. One of the limit theorems describes a longtime limit of a return probability, and the other presents a convergence in distribution for the position of the walker on a rescaled space by time. We find that the spatial entanglement generated by the threestate alternate DTQW is higher than that by the fourstate DTQW. Using all our results, we outline the relevance of these walks in threelevel physical systems.
 Publication:

Physical Review A
 Pub Date:
 December 2015
 DOI:
 10.1103/PhysRevA.92.062307
 arXiv:
 arXiv:1510.02885
 Bibcode:
 2015PhRvA..92f2307M
 Keywords:

 03.67.Lx;
 02.50.Cw;
 Quantum computation;
 Probability theory;
 Quantum Physics;
 Mathematics  Probability
 EPrint:
 11 pages, 7 figures