Structure of states which satisfy strong subadditivity of quantum entropy with equality

P Hayden, R Jozsa, AJ Winter

Research output: Contribution to journalArticle (Academic Journal)peer-review

220 Citations (Scopus)

Abstract

We give an explicit characterisation of the quantum states which saturate the strong subadditivity inequality for the von Neumann entropy. By combining a result of Petz characterising the equality case for the monotonicity of relative entropy with a recent theorem by Koashi and Imoto, we show that such states will have the form of a so-called short quantum Markov chain, which in turn implies that two of the systems are independent conditioned on the third, in a physically meaningful sense. This characterisation simultaneously generalises known necessary and sufficient entropic conditions for quantum error correction as well as the conditions for the achievability of the Holevo bound on accessible information.
Translated title of the contributionStructure of states which satisfy strong subadditivity of quantum entropy with equality
Original languageEnglish
Pages (from-to)359 - 374
JournalCommunications in Mathematical Physics
Volume246 (2)
Publication statusPublished - Apr 2004

Bibliographical note

Publisher: Springer-Verlag
Other identifier: IDS Number: 808IU

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