Groups and Operator Algebras Seminar

Speaker: Lyudmila Turowska (Chalmers University of Technology and University of Gothenburg)

Title: No-signaling quantum bicorrelations and quantum graph isomorphisms

Abstract: I will discuss quantum no-signaling correlations introduced by Duan and Winter and its different subclasses (quantum commuting, quantum and local). They will appear as strategies of non-local games with quantum inputs and quantum outputs. I will then introduce an analogue of bisynchronous correlations and characterise them by tracial states on the universal C*-algebra of the projective free unitary group, showing that in the quantum input/output setup, quantum permutations of finite sets must be replaced by quantum automorphisms of matrix algebras. As an application, I will discuss quantum graph isomorphisms by giving their non-local game interpretation, and compare our approach with the existing algebraic notions of quantum graph isomorphisms. In the case of classical graphs our operational notion of quantum isomorphism leads to new quantum symmetries.

This is a joint work with Michael Brannan, Sam Harris and Ivan Todorov.

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