Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
Abstract
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain models and is also supported by numerical studies of a variety of examples. In this paper we analyze the long-time behavior of a particular class of decoherent quantum walks, which, to the best of our knowledge, was only studied at the level of numerical simulations before. We consider a local coin operation which is randomly and independently chosen for each time step and each lattice site and prove that, under rather mild conditions, this leads to classical behavior: With the same scaling as needed for a classical diffusion the position distribution converges to a Gaussian, which is independent of the initial state. Our method is based on non-degenerate perturbation theory and yields an explicit expression for the covariance matrix of the asymptotic Gaussian in terms of the randomness parameters.
Keywords
Cite
@article{arxiv.1201.4839,
title = {Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations},
author = {Andre Ahlbrecht and Christopher Cedzich and Robert Matjeschk and Volkher B. Scholz and Albert H. Werner and Reinhard F. Werner},
journal= {arXiv preprint arXiv:1201.4839},
year = {2015}
}