Quantum association schemes

2024/04/09 by Daniel Gromada, Gromada, Daniel
Chemistry · Physics and Astronomy · #05C25 #05E30 #16T30 #18M40 #20G42 #Advanced Chemical Physics Studies #Combinatorics (math.CO) #FOS: Mathematics #History and advancements in chemistry #Molecular spectroscopy and chirality #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2404.06157

openalex publication_date 2024/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce quantum association schemes. This allows to define distance regular and strongly regular quantum graphs. We bring examples thereof. In addition, we formulate the duality for translation quantum association schemes corresponding to finite quantum groups.

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• Quantum structures from association schemes
• Subfactors from regular graphs induced by association schemes
• Quantum isomorphism of graphs from association schemes
• Quantum walks on simplexes and multiple perfect state transfer
• Quantum channels from association schemes