On the shape of correlation matrices for unitaries
DOI:
https://doi.org/10.7146/math.scand.a-142800Abstract
For a positive integer n, we study the collection Ffin(n) formed of all n×n matrices whose entries aij, 1≤i,j≤n, can be written as aij=τ(U∗jUi) for some n-tuple U1,U2,…,Un of unitaries in a finite-dimensional von Neumann algebra M with tracial state τ. We show that Ffin(n) is not closed for every n≥8. This improves a result by Musat and R{ø}rdam which states the same for n≥11.
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