Quantum majorization on semi-finite von Neumann algebras

Abstract

We extend Gour et al.'s characterization of quantum majorization via conditional min-entropy to the context of semi-finite von Neumann algebras. Our method relies on a connection between conditional min-entropy and the operator space projective tensor norm for injective von Neumann algebras. We then use this approach to generalize the tracial Hahn-Banach theorem of Helton, Klep and McCullough to vector-valued noncommutative L1-spaces.