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 -