In this talk, we will talk about two scaling problems — in particular the matrix scaling and its quantum generalization: operator scaling — and we will see how invariant theory can be used to rigorously analyze the convergence of the natural alternate minimization algorithms for these problems (and obtain different efficient algorithms for these). Then, time permitting, we will also see how operator scaling can be viewed as the dual of a natural entropic optimal transport problem.
Back to Workshop I: Optimal Transport for Density Operators: Theory and Numerics
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