Quantum Majorization on Semifinite von Neumann Algebras

TL;DR

This paper generalizes quantum majorization characterization to semifinite von Neumann algebras, linking conditional min-entropy with operator space tensor norms and connecting noncommutative analysis tools.

Contribution

It extends existing quantum majorization results to a broader algebraic setting using operator space theory and noncommutative $L_1$-spaces.

Findings

Established a connection between conditional min-entropy and tensor norms.

Extended quantum majorization characterization to semifinite von Neumann algebras.

Linked noncommutative vector-valued $L_1$-spaces with the tracial Hahn-Banach theorem.

Abstract

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 operator space projective tensor norm for injective von Neumann algebras. This approach also connects the tracial Hahn-Banach theorem of Helton, Klep and McCullough to noncommutative vector-valued $L_1$-space.