Details
| Original language | Undefined/Unknown |
|---|---|
| Pages (from-to) | 1219-1249 |
| Number of pages | 31 |
| Journal | Quantum Inf. Process. |
| Volume | 11 |
| Publication status | Published - 2012 |
Abstract
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In: Quantum Inf. Process., Vol. 11, 2012, p. 1219-1249.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
AU - Ahlbrecht, Andre
AU - Cedzich, Christopher
AU - Matjeschk, Robert
AU - Scholz, Volkher B.
AU - Werner, Albert H.
AU - Werner, Reinhard F.
N1 - Funding information: We gratefully acknowledge support by the DFG (Forschergruppe 635) and the EU
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
U2 - 10.1007/s11128-012-0389-4
DO - 10.1007/s11128-012-0389-4
M3 - Article
VL - 11
SP - 1219
EP - 1249
JO - Quantum Inf. Process.
JF - Quantum Inf. Process.
ER -