Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
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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.
Originalsprog | Engelsk |
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Tidsskrift | Quantum Information Processing |
Vol/bind | 11 |
Udgave nummer | 5 |
Sider (fra-til) | 1219-1249 |
Antal sider | 31 |
ISSN | 1570-0755 |
DOI | |
Status | Udgivet - okt. 2012 |
Eksternt udgivet | Ja |
ID: 256316998