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dc.contributor.authorAtserias, Albert
dc.contributor.authorMancinska, Laura
dc.contributor.authorRoberson, David E.
dc.contributor.authorSamal, Robert
dc.contributor.authorSeverini, Simone
dc.contributor.authorVarvitsiotis, Antonios
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Ciències de la Computació
dc.date.accessioned2019-01-28T11:43:48Z
dc.date.issued2019-05
dc.identifier.citationAtserias, A. [et al.]. Quantum and non-signalling graph isomorphisms. "Journal of combinatorial theory. Series B", vol. 136, Maig 2019, p. 289-328.
dc.identifier.issn0095-8956
dc.identifier.otherhttps://arxiv.org/abs/1611.09837
dc.identifier.urihttp://hdl.handle.net/2117/127696
dc.description.abstractWe introduce the (G,H)-isomorphism game, a new two-player non-local game that classical players can win with certainty iff the graphs G and H are isomorphic. We then define quantum and non-signalling isomorphisms by considering perfect quantum and non-signalling strategies for this game. We prove that non-signalling isomorphism coincides with fractional isomorphism, giving the latter an operational interpretation. We show that quantum isomorphism is equivalent to the feasibility of two polynomial systems obtained by relaxing standard integer programs for graph isomorphism to Hermitian variables. Finally, we provide a reduction from linear binary constraint system games to isomorphism games. This reduction provides examples of quantum isomorphic graphs that are not isomorphic, implies that the tensor product and commuting operator frameworks result in different notions of quantum isomorphism, and proves that both relations are undecidable.
dc.format.extent40 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica
dc.subject.lcshGraph theory
dc.subject.otherGraph isomorphism
dc.subject.otherQuantum strategies
dc.subject.otherNon-local games
dc.subject.otherEntanglement
dc.subject.otherNon-signalling
dc.subject.otherFractional isomorphism
dc.titleQuantum and non-signalling graph isomorphisms
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals
dc.identifier.doi10.1016/j.jctb.2018.11.002
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S0095895618301059
dc.rights.accessRestricted access - publisher's policy
drac.iddocument23565924
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020-648276-AUTAR
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/1PE/TIN2013-48031-C4-1-P
dc.date.lift2020-12-04
upcommons.citation.authorAtserias, A.; Mancinska, L.; Roberson, D.; Samal, R.; Severini, S.; Varvitsiotis, A.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameJournal of combinatorial theory. Series B
upcommons.citation.volume136
upcommons.citation.startingPage289
upcommons.citation.endingPage328
local.requestitem.embargadtrue


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