%0 Journal Article
%T Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
%A Andre Ahlbrecht
%A Christopher Cedzich
%A Robert Matjeschk
%A Volkher B. Scholz
%A Albert H. Werner
%A Reinhard F. Werner
%J Physics
%D 2012
%I arXiv
%R 10.1007/s11128-012-0389-4
%X 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.
%U http://arxiv.org/abs/1201.4839v1