The classification of geodesically convex trace functions with applications to the theory of multivariate operator means and quantum physics

The classification of geodesically convex trace functions with applications to the theory of multivariate operator means and quantum physics

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Frank Hansen, Tohoku University
Jadwin Hall 343

We consider trace functions generated by the functional calculus of a real function and obtain a complete characterization of the class of geodesically convex trace functions of this form. We then apply these results to the theory of multivariate operator means. Of particular interest is the calculation of the barycenter of relative entropy for a cluster of cubic states.