Simplicial techniques for operator solutions of linear constraint systems

buir.contributor.authorOkay, Cihan
buir.contributor.authorSikora, Igor
buir.contributor.orcidSikora, Igor|0000-0002-7655-4152
dc.citation.epage39
dc.citation.spage1
dc.citation.volumeNumber348
dc.contributor.authorChung, Ho Yiu
dc.contributor.authorOkay, Cihan
dc.contributor.authorSikora, Igor
dc.date.accessioned2025-02-28T11:20:30Z
dc.date.available2025-02-28T11:20:30Z
dc.date.issued2024-05-01
dc.departmentDepartment of Mathematics
dc.description.abstractA linear constraint system is specified by linear equations over the group Zd of integers modulo d. Their operator solutions play an important role in the study of quantum contextuality and non-local games. In this paper, we use the theory of simplicial sets to develop a framework for studying operator solutions of linear systems. Our approach refines the well-known group-theoretical approach based on solution groups by identifying these groups as algebraic invariants closely related to the fundamental group of a space. In this respect, our approach also makes a connection to the earlier homotopical approach based on cell complexes. Within our framework, we introduce a new class of linear systems that come from simplicial sets and show that any linear system can be reduced to one of that form. Then we specialize in linear systems that are associated with groups. We provide significant evidence for a conjecture stating that for odd devery linear system admitting a solution in a group admits a solution in Zd.
dc.embargo.release2026-05-01
dc.identifier.doi10.1016/j.topol.2024.108883
dc.identifier.eissn1879-3207
dc.identifier.issn0166-8641
dc.identifier.urihttps://hdl.handle.net/11693/116997
dc.language.isoEnglish
dc.publisherElsevier BV
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.topol.2024.108883
dc.rightsCC BY 4.0 DEED (Attribution 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleTopology and its Applications
dc.subjectLinear constraint systems
dc.subjectQuantum contextuality
dc.subjectSimplicial homotopy
dc.titleSimplicial techniques for operator solutions of linear constraint systems
dc.typeArticle

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