Quick Navigation

Overview Topics Abstract Importance Paper Tools References Reactions Discussion Publication Related

Topics

Quantum Foundations

Commutation Groups and State-Independent Contextuality

arXiv
Authors: Samson Abramsky, Serban-Ion Cercelescu, Carmen-Maria Constantin

Year

2026

Paper ID

28381

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

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 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.

Why This Paper Matters

  • This paper contributes to the Quantum Foundations research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • 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...

Paper Tools

Become a member to use research tools

Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.

Become a member Sign in
Show Paper arXiv Publisher Share Cite This Paper Copy URL Compare Copy DOI Add to Reading List Category Correction Request

References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.12197 [2] arXiv https://arxiv.org/abs/2603.12197 [3] Publisher https://arxiv.org/abs/2603.12197

Local Citation Graph (Related-Paper Links)

Current Paper #28381 #78817 Modelling Josephson Junctions w... #78814 Construction of isoscattering n... #78811 Autonomous Code Migration for Q... #78808 Experimental generation of asym...

External citation index: OpenAlex citation signal

Community Reactions

Quick sentiment from readers on this paper.

Score: 0
Likes: 0 Dislikes: 0

Sign in to react to this paper.

Discussion & Reviews (Moderated)

Average Rating: 0.0 / 5 (0 ratings)

No written reviews yet.