Approximate recovery and relative entropy I. general von Neumann subalgebras

TitleApproximate recovery and relative entropy I. general von Neumann subalgebras
Publication TypeJournal Article
Year of Publication2020
AuthorsFaulkner, T, Hollands, S, Swingle, B, Wang, Y
Date Published6/14/2020
Abstract

We prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I v. Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary v. Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. We comment on applications to the quantum null energy condition.

URLhttps://arxiv.org/abs/2006.08002