# Quantum structures from association schemes.

@article{Balu2019QuantumSF, title={Quantum structures from association schemes.}, author={Radhakrishnan Balu and Joseph W. Iverson}, journal={arXiv: Mathematical Physics}, year={2019} }

Starting from an association scheme induced by a finite group and the corresponding Bose-Mesner algebra we construct quantum Markov chains (QMC), their entangled versions, and interacting Fock spaces (IFS) using the quantum probabilistic approach. Our constructions are based on the intersection numbers and their duals Krien parameters of the schemes with examples focused on regular (distance-regular and distance-transitive) graphs.

#### One Citation

Quantum Probabilistic Spaces on Graphs for Topological Evolutions

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This work starts with the consideration of fusion rules of anyonic particles evolving on a 2D surface and the a hypergroup comes with it to construct entangled quantum Markov chains providing another perspective to topological computation. Expand

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