2026-07-29T10:45:17Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20357 2024-07-05T06:20:34Z ddc:004 open_access

Commutation Groups and State-Independent Contextuality Abramsky, Samson Cercelescu, Şerban-Ion Constantin, Carmen-Maria Contextuality state-independence quantum mechanics Pauli group group presentations unitary representations We introduce an algebraic structure for studying state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the well-known Peres-Mermin magic square, and used as a source of quantum advantage. We introduce commutation groups presented by generators and relations, and analyse them in terms of a string rewriting system. There is also a linear algebraic construction, a directed version of the Heisenberg group. We introduce contextual words as a general form of contextuality witness. We characterise when contextual words can arise in commutation groups, and explicitly construct non-contextual value assignments in other cases. We give unitary representations of commutation groups as subgroups of generalized Pauli n-groups. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Samson Abramsky and Şerban-Ion Cercelescu and Carmen-Maria Constantin 2024 Is Part Of LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2024.28 urn:nbn:de:0030-drops-203572 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.28 eng https://creativecommons.org/licenses/by/4.0/legalcode