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 - 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 \u201CGravitational Holography\u201D. 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.
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.
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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 -