Approximate recoverability and relative entropy II: 2-positive channels of general von Neumann algebras

Faulkner, Thomas; Hollands, Stefan

doi:10.1007/s11005-022-01510-9

Approximate recoverability and relative entropy II: 2-positive channels of general von Neumann algebras

Journal Article · Tue Mar 15 04:00:00 EDT 2022 · Letters in Mathematical Physics

DOI:https://doi.org/10.1007/s11005-022-01510-9· OSTI ID:1854955

Faulkner, Thomas; Hollands, Stefan

Abstract

We generalize our results in paper I in this series to quantum channels between general von Neumann algebras, proving the approximate recoverability of states which undergo a small change in relative entropy through the channel. To this end, we derive a strengthened form of the quantum data processing inequality for the change in relative entropy of two states under a channel between two von Neumann algebras. Compared to the usual inequality, there is an explicit lower bound involving the fidelity between the original state and a recovery channel.

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0019517

OSTI ID:: 1854955

Alternate ID(s):: OSTI ID: 1976697

Journal Information:: Letters in Mathematical Physics, Journal Name: Letters in Mathematical Physics Journal Issue: 2 Vol. 112; ISSN 0377-9017

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Netherlands

Language:: English

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