Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality

Patrick Hayden, Richard Jozsa, D. Petz, Andreas Winter

Research output: Contribution to journalArticle

194 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.

Original languageEnglish
Pages (from-to)359-374
Number of pages16
JournalCommunications in Mathematical Physics
Volume246
Issue number2
DOIs
Publication statusPublished - Apr 2004

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Quantum Entropy
Subadditivity
Equality
Quantum Error Correction
entropy
Relative Entropy
Markov chains
Quantum State
Monotonicity
Markov chain
theorems
Entropy
Sufficient
Imply
Generalise
Necessary
Theorem
Form

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality. / Hayden, Patrick; Jozsa, Richard; Petz, D.; Winter, Andreas.

In: Communications in Mathematical Physics, Vol. 246, No. 2, 04.2004, p. 359-374.

Research output: Contribution to journalArticle

Hayden, Patrick ; Jozsa, Richard ; Petz, D. ; Winter, Andreas. / Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality. In: Communications in Mathematical Physics. 2004 ; Vol. 246, No. 2. pp. 359-374.
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