Alternate two-dimensional quantum walk with a single-qubit coin

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dc.contributor.authorDi Franco, Carlo
dc.contributor.authorMc Gettrick, M.
dc.contributor.authorMachida, T.
dc.contributor.authorBusch, Thomas
dc.contributor.funderIrish Research Council for Science, Engineering and Technology
dc.contributor.funderScience Foundation Ireland
dc.date.accessioned2017-08-22T10:30:38Z
dc.date.available2017-08-22T10:30:38Z
dc.date.issued2011
dc.description.abstractWe 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.sponsorshipScience Foundation Ireland (05/IN/I852, 10/IN.1/I2979)en
dc.description.statusPeer revieweden
dc.description.versionPublished Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.articleid42337
dc.identifier.citationDi 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.84.042337en
dc.identifier.doi10.1103/PhysRevA.84.042337
dc.identifier.issn1050-2947
dc.identifier.issued4
dc.identifier.journaltitlePhysical Review Aen
dc.identifier.urihttps://hdl.handle.net/10468/4509
dc.identifier.volume84
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.urihttps://journals.aps.org/pra/abstract/10.1103/PhysRevA.84.042337
dc.rights© 2011, American Physical Societyen
dc.subjectTwo-dimensional quantum walken
dc.subjectGrover walken
dc.titleAlternate two-dimensional quantum walk with a single-qubit coinen
dc.typeArticle (peer-reviewed)en
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