Approximate recovery and relative entropy I. general von Neumann subalgebras

• URL: http://arxiv.org/abs/2006.08002v1
• Date: Sun, 14 Jun 2020 20:00:38 GMT
• Title: Approximate recovery and relative entropy I. general von Neumann subalgebras
• Authors: Thomas Faulkner, Stefan Hollands, Brian Swingle, Yixu Wang
• Abstract summary: 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 results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda $L_p$ norms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $L_p$ norms. We comment on applications to the quantum null energy condition.

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