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 von Neumann subalgebra when change in relative entropy, with respect to fixed reference state, is small. Our result generalization previous results applied type-I algebras by Junge at al. [ arXiv:1509.07127 ]. broadly follow their proof strategy but consider here arbitrary algebras, where qualitatively new issues arise. hinge construction certain analytic vectors and computations/estimations Araki–Masuda $$L_p$$ L p norms. comment applications quantum null energy condition.