Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

Abstract We prove the existence of a universal recovery channel that approximately recovers states on a von 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 von Neumann algebras by Junge at al. arXiv: 1509. 07127. We broadly follow their proof strategy but consider here arbitrary von 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 L p norms. We comment on applications to the quantum null energy condition.