  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 $L_p$ norms. We comment on
applications to the quantum null energy condition.
