Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

Faulkner, Thomas; Hollands, Stefan; Swingle, Brian; Wang, Yixu

doi:10.1007/s00220-021-04143-6

Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

Journal Article · Mon Jan 03 00:00:00 EST 2022 · Communications in Mathematical Physics

DOI:https://doi.org/10.1007/s00220-021-04143-6· OSTI ID:1843330

Faulkner, Thomas ^[1]; Hollands, Stefan ^[2]; Swingle, Brian ^[3]; Wang, Yixu ^[3]

Univ. of Illinois at Urbana-Champaign, IL (United States); IL and KITP, Santa Barbara, CA (United States); UIUC
Univ. Leipzig (Germany); KITP, Santa Barbara, CA (United States)
Univ. of Maryland, College Park, MD (United States)

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

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0019517

OSTI ID:: 1843330

Journal Information:: Communications in Mathematical Physics, Journal Name: Communications in Mathematical Physics Journal Issue: 1 Vol. 389; ISSN 0010-3616

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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