Bisynchronicity for quantum input-quantum output correlations and generalized quantum automorphisms of graphs.

Michael Brannan (University of Waterloo)

Thursday 1st December 16:00-17:00 Maths 311B

Abstract

In quantum information theory, the bisynchronous correlations form an interesting class of bipartite no-signaling correlations where Alice and Bob's joint input-output behaviour is correlated in such a way that it looks as though Alice and Bob are both using a common injective function to prescribe outputs to inputs.  In this talk, I will review some interesting operator algebraic characterizations of bisynchronous correlations, and then I will move on to talk about what it means for a correlation to be bisynchronous when we allow more general bipartite quantum states as inputs and outputs.  In this more general setup, it turns out that out that the quantum permutation matrices (that play such a big role in the theory of bisynchronous correlations) need to be replaced by quantum automorphisms of matrix algebras.   I'll explain how these considerations in the context of graph isomorphism games give rise to a seemingly mysterious new class of quantum groups which act as generalized (or ``fuzzy'') quantum automorphisms of the underlying graphs.  This is joint work with S. Harris, I. Todorov, and L. Turowska.

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