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

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dc.contributor.author Di Franco, Carlo
dc.contributor.author Mc Gettrick, M.
dc.contributor.author Machida, T.
dc.contributor.author Busch, Thomas
dc.date.accessioned 2017-08-22T10:30:38Z
dc.date.available 2017-08-22T10:30:38Z
dc.date.issued 2011
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.volume 84
dc.identifier.issued 4
dc.identifier.issn 1050-2947
dc.identifier.uri http://hdl.handle.net/10468/4509
dc.identifier.doi 10.1103/PhysRevA.84.042337
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.format.mimetype application/pdf en
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
dc.internal.authorcontactother Thomas Busch, Physics, University College Cork, Cork, Ireland. +353-21-490-3000. Email: thbusch@phys.ucc.ie en
dc.internal.availability Full text available en
dc.description.version Published Version en
dc.internal.wokid WOS:000296283900004
dc.contributor.funder Irish Research Council for Science, Engineering and Technology
dc.contributor.funder Science Foundation Ireland
dc.description.status Peer reviewed en
dc.identifier.journaltitle Physical Review A en
dc.internal.IRISemailaddress thbusch@phys.ucc.ie en
dc.identifier.articleid 42337


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