Random quantum graphs

Mateusz Wasilewski (KU Leuven)

Thursday 25th February 16:00-17:00 Please contact the organizers for Zoom coordinates

Abstract

The study of quantum graphs emerged from quantum information theory. One way to define them is to replace the space of functions on a vertex set of a classical graph with a noncommutative algebra and find a satisfactory counterpart of an adjacency matrix in this context. Another approach is to view undirected graphs as symmetric, reflexive relations and "quantize" the notion of a relation on a set. In this case, quantum graphs are operator systems and the definitions are equivalent. Doing this has some consequences already for classical graphs; viewing them as operator systems of a special type has already led to the introduction of a few new "quantum" invariants.

Motivated by developing the general theory of quantum graphs, I will take a look at random quantum graphs, having in mind that the study of random classical graphs is very fruitful. I will show how having multiple perspectives on the notion of a quantum graph is useful in determining the symmetries of these objects – as expected, a generic quantum graph is asymmetric.

Joint work with Alexandru Chirvasitu.

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