TY - JOUR

T1 - Approximate Recovery and Relative Entropy I

T2 - General von Neumann Subalgebras

AU - Faulkner, Thomas

AU - Hollands, Stefan

AU - Swingle, Brian

AU - Wang, Yixu

N1 - Funding Information:
SH is grateful to the Max-Planck Society for supporting the collaboration between MPI-MiS and Leipzig U., grant Proj. Bez. M.FE.A.MATN0003. TF and SH benefited from the KITP program “Gravitational Holography”. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. BGS and YW acknowledge that this material is based in part on work supported by the Simons Foundation as part of the It From Qubit Collaboration and in part on work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0360. YW would like to acknowledge discussions with Jonathan Rosenberg. TF acknowledges part of the work presented here is support by the DOE under grant DE-SC0019517.
Publisher Copyright:
© 2021, The Author(s).

PY - 2022/1

Y1 - 2022/1

N2 - 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 norms. We comment on applications to the quantum null energy condition.

AB - 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 norms. We comment on applications to the quantum null energy condition.

UR - http://www.scopus.com/inward/record.url?scp=85122230411&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85122230411&partnerID=8YFLogxK

U2 - 10.1007/s00220-021-04143-6

DO - 10.1007/s00220-021-04143-6

M3 - Article

AN - SCOPUS:85122230411

SN - 0010-3616

VL - 389

SP - 349

EP - 397

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -