The generator and quantum Markov semigroup for quantum walks
Mathematical Physics
2013-05-09 v1 math.MP
Abstract
The quantum walks in the lattice spaces are represented as unitary evolutions. We find a generator for the evolution and apply it to further understand the walks. We first extend the discrete time quantum walks to continuous time walks. Then we construct the quantum Markov semigroup for quantum walks and characterize it in an invariant subalgebra. In the meanwhile, we obtain the limit distributions of the quantum walks in one-dimension with a proper scaling, which was obtained by Konno by a different method.
Cite
@article{arxiv.1305.1749,
title = {The generator and quantum Markov semigroup for quantum walks},
author = {Chul Ki Ko and Hyun Jae Yoo},
journal= {arXiv preprint arXiv:1305.1749},
year = {2013}
}
Comments
24 pages, 8 figures, to appear in Kodai Mathematical Journal