Topological methods for studying contextuality: N-Cycle scenarios and beyond

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buir.contributor.authorKharoof, Aziz
buir.contributor.authorİpek, Selman
buir.contributor.authorOkay, Cihan
buir.contributor.orcidKharoof, Aziz|0000-0002-4010-6526
buir.contributor.orcidİpek, Selman|0000-0002-4475-4221
buir.contributor.orcidOkay, Cihan|0000-0001-8097-5227
dc.citation.epage1127-34en_US
dc.citation.issueNumber8
dc.citation.spage1127-1
dc.citation.volumeNumber25
dc.contributor.authorKharoof, Aziz
dc.contributor.authorİpek, Selman
dc.contributor.authorOkay, Cihan
dc.date.accessioned2024-03-06T08:26:59Z
dc.date.available2024-03-06T08:26:59Z
dc.date.issued2023-07-27
dc.departmentDepartment of Mathematics
dc.description.abstractSimplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize nonsignaling distributions on contextuality scenarios. This paper studies simplicial distributions on two-dimensional measurement spaces by introducing new topological methods. Two key ingredients are a geometric interpretation of Fourier–Motzkin elimination and a technique based on the collapsing of measurement spaces. Using the first one, we provide a new proof of Fine’s theorem characterizing noncontextual distributions in N-cycle scenarios. Our approach goes beyond these scenarios and can describe noncontextual distributions in scenarios obtained by gluing cycle scenarios of various sizes. The second technique is used for detecting contextual vertices and deriving new Bell inequalities. Combined with these methods, we explore a monoid structure on simplicial distributions.
dc.identifier.doi10.3390/e25081127
dc.identifier.eissn1099-4300
dc.identifier.urihttps://hdl.handle.net/11693/114356
dc.language.isoEnglish
dc.publisherMDPI AG
dc.relation.isversionofhttps://doi.org/10.3390/e25081127
dc.rightsCC BY 4.0 DEED (Attribution 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleEntropy
dc.subjectQuantum information
dc.subjectQuantum contextuality
dc.subjectQuantum nonlocality
dc.subjectAlgebraic topology
dc.titleTopological methods for studying contextuality: N-Cycle scenarios and beyond
dc.typeArticle

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