Vertex-transitive quantum graphs

arXiv:2605.30730 · math.OA, math.CO, math.QA, quant-ph · Submitted 2026-05-29 · Read on arXiv

math.OA, math.CO, math.QA, quant-ph

Submitted: 2026-05-29

Updated: 2026-09-24

Comments: 29 pages, 4 figures; corrected a propagating typo in the expression for VT^3_4

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Generalization — 6× in this paper · explained in 13 episodes
• Entanglement — 2× in this paper · explained in 3 episodes
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Distillation — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Quantum-rigid random quantum graphs
• Quantum graphs in infinite-dimensions: Hilbert--Schmidts and Hilbert modules
• Quantum graphs of homomorphisms

Related papers

• The Differential Structure of Generators of KMS-Symmetric Quantum Markov Semigroups
• A complete characterization of eventually entanglement breaking unital quantum channels
• Quantum channels on duals of von Neumann algebras in the Schr" o dinger picture
• Quantum Graph Theory by Example
• Anti-isomorphisms and the naturality of channel--state duality