Communications in Mathematical Physics

, Volume 246, Issue 2, pp 359–374 | Cite as

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

  • Patrick Hayden
  • Richard Jozsa
  • Dénes Petz
  • Andreas WinterEmail author


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.


Entropy Markov Chain Quantum State Error Correction Relative Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Patrick Hayden
    • 1
  • Richard Jozsa
    • 2
  • Dénes Petz
    • 3
  • Andreas Winter
    • 2
    • 4
    Email author
  1. 1.Institute for Quantum InformationPasadenaUSA
  2. 2.Department of Computer ScienceUniversity of BristolBristolU.K
  3. 3.Department for Mathematical AnalysisMathematical Institute, Budapest University of Technology and EconomicsBudapestHungary
  4. 4.Department of MathematicsUniversity of Bristol, University WalkBristolU.K

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