Andreas Bluhm: [WS1] Quantifying measurement incompatibility with matrix convex sets

Speaker
Andreas Bluhm, Université Grenoble Alpes, CNRS, LIG

Abstract
In this talk we will review a connection between two very different problems: the compatibility of measurements in quantum information theory and the membership in certain minimal matrix convex sets. Moreover, the minimal amount of noise necessary to render any tuple of measurements (in fixed dimension and with a fixed number of outcomes) compatible corresponds to the size difference between certain minimal and maximal matrix convex sets. In order to compute the noise robustness of measurement incompatibility, we put forward hierarchies of semi-definite programs and demonstrate their usefulness with some examples. Finally, we will use the structure of the different types of extreme points of the matrix convex sets involved to further study the resulting optimization problems.