Quantum Majorization on Semifinite von Neumann Algebras

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.

arXiv comment39 pages. Comments are welcome!

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Cited by in corpus (3)

• A general theory of comparison of quantum channels (and beyond)
• Quantum teleportation in the commuting operator framework
• Asymptotic Equipartition Theorems in von Neumann algebras