Variational approach to relative entropies with an application to QFT

Hollands, Stefan

doi:10.1007/s11005-021-01474-2

Variational approach to relative entropies with an application to QFT

Journal Article · Sat Oct 30 00:00:00 EDT 2021 · Letters in Mathematical Physics

DOI:https://doi.org/10.1007/s11005-021-01474-2· OSTI ID:1828397

Hollands, Stefan

Abstract

We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

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Sponsoring Organization:: USDOE

OSTI ID:: 1828397

Journal Information:: Letters in Mathematical Physics, Journal Name: Letters in Mathematical Physics Journal Issue: 6 Vol. 111; ISSN 0377-9017

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Netherlands

Language:: English

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