Commutation Groups and State-Independent Contextuality

• URL: http://arxiv.org/abs/2603.12197v2
• Date: Fri, 13 Mar 2026 13:57:17 GMT
• Title: Commutation Groups and State-Independent Contextuality
• Abstract summary: We study state-independent contextuality arguments, a key form of quantum non-classicality exemplified by the Peres-Mermin magic square.<n>We introduce emphcommutation groups presented by generators and relations, and analyse them in terms of a string rewriting system.<n>There is also a linear algebraic construction, a directed version of the Heisenberg group.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 \emph{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 \emph{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.

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