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Logic Seminar: Combinatorial approximations of matrix traces (Peter Burton)

Author: Lona

Speaker: Peter Burton

Abstract: Abstract: This talk will exposit a combinatorial approach to certain topics involving the normalized traces of unitary matrices. By a normalized trace, we mean the standard trace divided by the dimension of the matrix. This normalization turns out to profoundly change the nature of questions about how to realize configurations of traces, and can be understood as a way of passing from noncommutative measure theory to noncommutative probability theory. The latter area is the framework for much of quantum information theory and, in particular, for the well-known Connes’ embedding conjecture which will be the subject of our second talk. The perspective we will present is that dealing with matrices and traces is somewhat unnecessary and all the relevant ideas can be expressed in terms of labelings of finite graphs.