On the degree of regular quantum graphs

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• Junichiro Matsuda (University of Waterloo)
• Tuesday 03 December 2024, 09:00-10:00
• Seminar Room 1, Newton Institute.

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QIAW02 - New trends at the intersection of quantum information theory, quantum groups and operator algebras

The theory of quantum graphs has developed in the last decade due to the interaction between quantum information theory, quantum groups, and operator algebras. It is natural to expect regular quantum graphs to admit spectral characterization of their properties as classical graphs do.  The degree of a regular finite quantum graph may not be an integer in general because it is just an eigenvalue of the adjacency matrix and we can no longer count the number of edges one by one. However, in the tracial case, we obtained that the degree is indeed an integer. The clue is a characterization of regularity in terms of the operator bimodule associated with the quantum graph.This is a joint work with Matthew Kennedy and Larissa Kroell.

This talk is part of the Isaac Newton Institute Seminar Series series.

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