Propagating quantum walks: The origin of interference structures |
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| Authors: | Peter L Knight Eugenio Roldán J E Sipe |
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| Affiliation: | 1. Optics Section, Blackett Laboratory , Imperial College London , London, SW7 2AZ, UK E-mail: p.knight@imperial.ac.uk;2. Departament d'òptica , Universitat de València , Dr. Moliner 50, 46100, Burjassot, Spain E-mail: eugenio.roldan@uv.es;3. Department of Physics , University of Toronto , Toronto, M5S 1A7, Canada E-mail: sipe@physics.utoronto.ca |
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| Abstract: | Abstract We analyse 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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