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On the first two moments of quantum random walks in one dimensional lattice
by
Chaobin Liu
Bowie State University, Bowie, MD 21046
Consider the quantum random walks in one dimensional lattice determined by a 2×2 unitary matrix U(k). Using some analytic properties of U(k), we show how the first two moments of the position probability distribution is determined by the eigenvalues of U(k). This approach simplifies and clarifies certain prior derivations based on Fourier transform methods. We derive that the maximum leading term of the standard deviation of (X_t) is t. This maximum leading term is achievable only when the coin operator A is diagonal and the initial state is unbiased. Starting in the classical state 0R, we infer that the maximum leading term of the standard deviation of (X_t) is t/2. We further show the maximum leading term t/2 is achievable using some known examples.
Date received: February 14, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caws-28.