Relativistic quantum walks
arXiv:quant-ph/0508096 · doi:10.1103/PhysRevA.73.054302
Abstract
By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum walker, initially localized on a lattice, is directly analogous to relativistic wave-packet spreading. Analytic wave-packet solutions reveal a striking connection between the discrete and continuous time quantum walks.
4 pages, 4 figures, published and corrected version
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