Quantum random walks and piecewise deterministic evolutions

Blanchard P, Hongler MO (2004)
PHYSICAL REVIEW LETTERS 92(12).

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In the continuous space and time limit, we show that the probability density to find the quantum random walk (QRW) driven by the Hadamard "coin" solves a hyperbolic evolution equation similar to the one obtained for a random two-velocity evolution with spatially inhomogeneous transition rates between the velocity states. In spite of the presence of a nonlinear drift term, it is remarkable that the QRW position can easily be described in simple analytical terms. This allows us to derive the quadratic time dependence of the variance typical for the QRW.
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Blanchard P, Hongler MO. Quantum random walks and piecewise deterministic evolutions. PHYSICAL REVIEW LETTERS. 2004;92(12).
Blanchard, P., & Hongler, M. O. (2004). Quantum random walks and piecewise deterministic evolutions. PHYSICAL REVIEW LETTERS, 92(12).
Blanchard, P., and Hongler, M. O. (2004). Quantum random walks and piecewise deterministic evolutions. PHYSICAL REVIEW LETTERS 92.
Blanchard, P., & Hongler, M.O., 2004. Quantum random walks and piecewise deterministic evolutions. PHYSICAL REVIEW LETTERS, 92(12).
P. Blanchard and M.O. Hongler, “Quantum random walks and piecewise deterministic evolutions”, PHYSICAL REVIEW LETTERS, vol. 92, 2004.
Blanchard, P., Hongler, M.O.: Quantum random walks and piecewise deterministic evolutions. PHYSICAL REVIEW LETTERS. 92, (2004).
Blanchard, Philippe, and Hongler, MO. “Quantum random walks and piecewise deterministic evolutions”. PHYSICAL REVIEW LETTERS 92.12 (2004).
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