Solution group representations as quantum symmetries of graphs

David E. Roberson, Simon Schmidt*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that the quantum automorphism group of such a colored graph is the dual of the homogeneous solution group of the underlying linear constraint system. Given a vertex- and edge-colored graph with certain properties, we construct an uncolored graph that has the same quantum automorphism group as the colored graph we started with. Using those results, we obtain the first-known example of a graph that has quantum symmetry and finite quantum automorphism group. Furthermore, we construct a pair of quantum isomorphic, non-isomorphic graphs that both have no quantum symmetry.

Original languageEnglish
JournalJournal of the London Mathematical Society
Volume106
Issue number4
Pages (from-to)3379-3410
ISSN0024-6107
DOIs
Publication statusPublished - 2022

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