This paper connects the concept of a "zonoid" from convex geometry (a zonoid is (possibly continuous) sum of segments) and the concept of "distinguashibility norms" associated to a quantum measurement, from quantum information theory. This connection allows to import powerful probabilistic techniques from Banach space theory to prove new and optimal sparsification results for quantum measurements.
E-mail :
aubrun (arrobas) math. univ-lyon1. fr