Strong convergence of quantum random walks via semigroup decomposition
Probability
2018-06-07 v4 Mathematical Physics
Functional Analysis
math.MP
Abstract
We give a simple and direct treatment of the strong convergence of quantum random walks to quantum stochastic operator cocycles, via the semigroup decomposition of such cocycles. Our approach also delivers convergence of the pointwise product of quantum random walks to the quantum stochastic Trotter product of the respective limit cocycles, thereby revealing the algebraic structure of the limiting procedure. The repeated quantum interactions model is shown to fit nicely into the convergence scheme described.
Keywords
Cite
@article{arxiv.1712.02848,
title = {Strong convergence of quantum random walks via semigroup decomposition},
author = {Alexander C. R. Belton and Michal Gnacik and J. Martin Lindsay},
journal= {arXiv preprint arXiv:1712.02848},
year = {2018}
}
Comments
29 pages. To appear in the journal Annales Henri Poincare. Revisions made in v2; typos corrected in v3; final correction in v4