Commutation Groups and State-Independent Contextuality
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917337530105856 |
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| author | Abramsky, Samson Cercelescu, Serban-Ion Constantin, Carmen-Maria |
| author_facet | Abramsky, Samson Cercelescu, Serban-Ion Constantin, Carmen-Maria |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Commutation Groups and State-Independent Contextuality Abramsky, Samson Cercelescu, Serban-Ion Constantin, Carmen-Maria Quantum Physics Logic in Computer Science 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. |
| title | Commutation Groups and State-Independent Contextuality |
| topic | Quantum Physics Logic in Computer Science |
| url | https://arxiv.org/abs/2603.12197 |