Alternate two-dimensional quantum walk with a single-qubit coin
dc.contributor.author | Di Franco, Carlo | |
dc.contributor.author | Mc Gettrick, M. | |
dc.contributor.author | Machida, T. | |
dc.contributor.author | Busch, Thomas | |
dc.contributor.funder | Irish Research Council for Science, Engineering and Technology | |
dc.contributor.funder | Science Foundation Ireland | |
dc.date.accessioned | 2017-08-22T10:30:38Z | |
dc.date.available | 2017-08-22T10:30:38Z | |
dc.date.issued | 2011 | |
dc.description.abstract | We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and Th. Busch, Phys. Rev. Lett. 106, 080502 (2011)]. For a particular initial state of the coin, this walk is able to perfectly reproduce the spatial probability distribution of the nonlocalized case of the Grover walk. Here, we present a more detailed proof of this equivalence. We also extend the analysis to other initial states in order to provide a more complete picture of our walk. We show that this scheme outperforms the Grover walk in the generation of x-y spatial entanglement for any initial condition, with the maximum entanglement obtained in the case of the particular aforementioned state. Finally, the equivalence is generalized to wider classes of quantum walks and a limit theorem for the alternate walk in this context is presented. | en |
dc.description.sponsorship | Science Foundation Ireland (05/IN/I852, 10/IN.1/I2979) | en |
dc.description.status | Peer reviewed | en |
dc.description.version | Published Version | en |
dc.format.mimetype | application/pdf | en |
dc.identifier.articleid | 42337 | |
dc.identifier.citation | Di Franco, C., Mc Gettrick, M., Machida, T. and Busch, T. (2011) 'Alternate two-dimensional quantum walk with a single-qubit coin', Physical Review A, 84(4), 042337 (8pp). doi: 10.1103/PhysRevA.84.042337 | en |
dc.identifier.doi | 10.1103/PhysRevA.84.042337 | |
dc.identifier.issn | 1050-2947 | |
dc.identifier.issued | 4 | |
dc.identifier.journaltitle | Physical Review A | en |
dc.identifier.uri | https://hdl.handle.net/10468/4509 | |
dc.identifier.volume | 84 | |
dc.language.iso | en | en |
dc.publisher | American Physical Society | en |
dc.relation.uri | https://journals.aps.org/pra/abstract/10.1103/PhysRevA.84.042337 | |
dc.rights | © 2011, American Physical Society | en |
dc.subject | Two-dimensional quantum walk | en |
dc.subject | Grover walk | en |
dc.title | Alternate two-dimensional quantum walk with a single-qubit coin | en |
dc.type | Article (peer-reviewed) | en |
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