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arXiv · 1201.4839

Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations

Andre Ahlbrecht·Christopher Cedzich·Robert Matjeschk·Volkher B. Scholz·Albert H. Werner·Reinhard F. Werner
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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.

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Andre Ahlbrecht, Christopher Cedzich, Robert Matjeschk, Volkher B. Scholz, Albert H. Werner, Reinhard F. Werner. 2012-01-23. Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations. https://doi.org/10.1007/s11128-012-0389-4

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