Quantization and Asymptotic Behaviour of ${\epsilon }_{V^k}$ Quantum Random Walk on Integers

Abstract

Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the ${\epsilon }_{V^k}$ walk, has the novel feature that it uses many identical quantum coins keeping at the same time characteristic quantum features like the quadratically faster than the classical spreading rate, and unexpected distribution cutoffs. A weak limit of the position probability distribution (pd) is obtained, and universal properties of this arch sine asymptotic distribution function are examined. Questions of driving the walk are investigated by means of a quantum optical interaction model that reveals robustness of quantum features of walker's asymptotic pd, against stimulated and spontaneous quantum noise on the coin system.

11 pages, no figures Submitted to Proc. of 3rd NEXT Sigma-Phi, Kolymbari Aug. 2005, Eds. G. Kaniadakis, A. Carbone, M. Lissia

References in corpus (9)

• Quantum random walks - an introductory overview
• A Quantum Random Walk Search Algorithm
• Spatial search by quantum walk
• From quantum cellular automata to quantum lattice gases
• Implementing the quantum random walk
• Quantum random walks in optical lattices
• Weak limits for quantum random walks
• Pseudo Memory Effects, Majorization and Entropy in Quantum Random Walks
• Asymptotics of Quantum Random Walk Driven by Optical Cavity

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