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.

1 aFaulkner, Thomas1 aHollands, Stefan1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/2006.0800201128nas a2200145 4500008004100000245008100041210006900122260001400191520066400205100002100869700002100890700001900911700001500930856003700945 2020 eng d00aApproximate recovery and relative entropy I. general von Neumann subalgebras0 aApproximate recovery and relative entropy I general von Neumann c6/14/20203 aWe 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.

1 aFaulkner, Thomas1 aHollands, Stefan1 aSwingle, Brian1 aWang, Yixu uhttps://arxiv.org/abs/2006.08002