The exact quantum chromatic number of Hadamard graphs and their products

Abstract: Quantum chromatic numbers are defined via non-local games on classical graphs. Very few exact computations of the quantum chromatic number of graphs are known. In this talk, we will give a proof of the exact quantum chromatic number of Hadamard graphs. As opposed to prior results on this problem, this approach uses results on conjugacy class graphs which allows us to consider products of Hadamard graphs as well. Specifically, we compute the exact quantum chromatic number of categorical products of Hadamard graphs.

Throughout this work, we use several results for the quantum chromatic numbers of quantum graphs, an operator algebraic generalization of classical graphs that appears in connection to quantum information theory. In particular, we also discuss results on products of quantum graphs appearing in joint work with Rolando de Santiago.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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