The concept of matrix majorization has been recently generalized, in a natural way, to the quantum-mechanical setting by Gour, Jennings, Buscemi, Duan, and Marvian; the notion is referred to as "quantum majorization" and has been used to accommodate the ordering of bipartite quantum states and quantum processes (i.e. CPTP maps) in quantum mechanical systems. They established an entropic characterization of quantum majorization (for finite-dimensions).

We extend Gour et al's characterization of quantum majorization via conditional min-entropy to the context of semifinite 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.

This is a joint work with Priyanga Ganesan, Li Gao, and Sarah Plosker.