Commutation Groups and State-Independent Contextuality

Authors Samson Abramsky , Şerban-Ion Cercelescu, Carmen-Maria Constantin

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Samson Abramsky
  • Department of Computer Science, University College London, London, UK
Şerban-Ion Cercelescu
  • Department of Computer Science, University of Oxford, Oxford, UK
Carmen-Maria Constantin
  • Department of Computer Science, University College London, London, UK

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Samson Abramsky, Şerban-Ion Cercelescu, and Carmen-Maria Constantin. Commutation Groups and State-Independent Contextuality. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation
  • Contextuality
  • state-independence
  • quantum mechanics
  • Pauli group
  • group presentations
  • unitary representations


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