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Quantum random walks in one dimension via generating functions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007) Cet article a éte moissonné depuis la source Episciences

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We analyze nearest neighbor one-dimensional quantum random walks with arbitrary unitary coin-flip matrices. Using a multivariate generating function analysis we give a simplified proof of a known phenomenon, namely that the walk has linear speed rather than the diffusive behavior observed in classical random walks. We also obtain exact formulae for the leading asymptotic term of the wave function and the location probabilities. 
@article{DMTCS_2007_special_253_a15,
     author = {Bressler, Andrew and Pemantle, Robin},
     title = {Quantum random walks in one dimension via generating functions},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2007},
     volume = {DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)},
     doi = {10.46298/dmtcs.3533},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3533/}
}
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Bressler, Andrew; Pemantle, Robin. Quantum random walks in one dimension via generating functions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07), DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) (2007). doi: 10.46298/dmtcs.3533

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