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dc.creatorFan, S
dc.creatorFeng, Z
dc.creatorXiong, S
dc.creatorYang, WS
dc.date.accessioned2021-02-04T21:36:24Z
dc.date.available2021-02-04T21:36:24Z
dc.date.issued2011-10-10
dc.identifier.issn1050-2947
dc.identifier.issn1094-1622
dc.identifier.doihttp://dx.doi.org/10.34944/dspace/6007
dc.identifier.other831EY (isidoc)
dc.identifier.urihttp://hdl.handle.net/20.500.12613/6025
dc.description.abstractIn this paper, we study the discrete-time quantum random walks on a line subject to decoherence. The convergence of the rescaled position probability distribution p(x,t) depends mainly on the spectrum of the superoperator L kk. We show that if 1 is an eigenvalue of the superoperator with multiplicity one and there is no other eigenvalue whose modulus equals 1, then P(ν√t,t) converges to a convex combination of normal distributions. In terms of position space, the rescaled probability mass function p t(x,t)≡p(√tx,t), x Z/√t, converges in distribution to a continuous convex combination of normal distributions. We give a necessary and sufficient condition for a U(2) decoherent quantum walk that satisfies the eigenvalue conditions. We also give a complete description of the behavior of quantum walks whose eigenvalues do not satisfy these assumptions. Specific examples such as the Hadamard walk and walks under real and complex rotations are illustrated. For the O(2) quantum random walks, an explicit formula is provided for the scaling limit of p(x,t) and their moments. We also obtain exact critical exponents for their moments at the critical point and show universality classes with respect to these critical exponents. © 2011 American Physical Society.
dc.format.extent042317-
dc.language.isoen
dc.relation.haspartPhysical Review A - Atomic, Molecular, and Optical Physics
dc.relation.isreferencedbyAmerican Physical Society (APS)
dc.subjectmath.PR
dc.subjectmath.PR
dc.titleConvergence of quantum random walks with decoherence
dc.typeArticle
dc.type.genreJournal Article
dc.relation.doi10.1103/PhysRevA.84.042317
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.date.updated2021-02-04T21:36:21Z
refterms.dateFOA2021-02-04T21:36:24Z


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