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arXiv · 2603.12197

Commutation Groups and State-Independent Contextuality

Samson Abramsky·Serban-Ion Cercelescu·Carmen-Maria Constantin
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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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Samson Abramsky, Serban-Ion Cercelescu, Carmen-Maria Constantin. 2026-03-12. Commutation Groups and State-Independent Contextuality. https://arxiv.org/abs/2603.12197

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