Classification of Quantum Graphs on $M_2$ and their Quantum Automorphism Groups

Junichiro Matsuda

doi:10.1063/5.0081059

paper

Classification of Quantum Graphs on $M_{2}$ and their Quantum Automorphism Groups

arXiv:2110.09085 · doi:10.1063/5.0081059

Abstract

Motivated by string diagrammatic approach to undirected tracial quantum graphs by Musto, Reutter, Verdon (2018), in the former part of this paper we diagrammatically formulate directed nontracial quantum graphs by Brannan, Chirvasitu, Eifler, Harris, Paulsen, Su, Wasilewski (2019). In the latter part, we supply a concrete classification of undirected reflexive quantum graphs on $M_{2}$ and their quantum automorphism groups in both tracial and nontracial settings. We also obtain quantum isomorphisms between tracial quantum graphs on $M_{2}$ and certain classical graphs, which reproves the monoidal equivalences between $S O (3)$ and $S_{4}^{+}$ , and $O (2)$ and $H_{2}^{+}$ .

44 pages; typos corrected

Classification of Quantum Graphs on $M_{2}$ and their Quantum Automorphism Groups

Abstract

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Classification of Quantum Graphs on M2​ and their Quantum Automorphism Groups

Abstract

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Classification of Quantum Graphs on $M_{2}$ and their Quantum Automorphism Groups