Quantum Automorphism Groups of Hypergraphs

Nicolas Faro{\ss}

Quantum Automorphism Groups of Hypergraphs

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arxiv 2405.09894 v2 pith:XKDPT4CA submitted 2024-05-16 math.OA math.QA

Nicolas Faro{ss} This is my paper · ORCID

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keywords automorphismquantumgroupalgebrashypergraphsactionactsbichon

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We introduce a quantum automorphism group for hypergraphs, which turns out to generalize the quantum automorphism group of Bichon for classical graphs. Further, we show that our quantum automorphism group acts on hypergraph C*-algebras as recently defined. In particular, this action generalizes the one on graph C*-algebras by Schmidt-Weber in 2018.

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Existence and nonexistence of commutativity gadgets for entangled CSPs
quant-ph 2025-09 conditional novelty 8.0 of 10

A CSP whose quantum endomorphism monoid is non-classical admits no commutativity gadget; in particular, k-colouring for k at least 4 has no commutativity gadget, while an oracular commutativity gadget exists.

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