Propagating Quantum Walks: the origin of interference structures

Details Propagating Quantum Walks: the origin of interference structures Propagating Quantum Walks: the origin of interference structures

2003-12-15

arxiv.org/abs/quant-ph/0312133v1

J. Mod. Opt. 51 (2004) 1761-1777

Physics

Quantum Physics

17 pages, 3 figures. Submitted to Journal of Modern Optics

Scientific paper

We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The particular way of deriving the solution allows a rigorous derivation of a long wavelength approximation. This long wavelength approximation is useful as it provides an approximate analytical expression that captures the basics of the quantum walk and allows us to gain insight into the physics of the process.

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