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Hierarchy of graph-diagonal states based on quantum discord and entanglement classification

  • Mohammad Ali Jafarizadeh
  • Naser KarimiEmail author
  • Davood Amidi Sahlan
  • Ahmad Heshmati
  • Marziyeh Yahyavi
Regular Article

Abstract

For the relative entropy-based measure of quantum discord the key idea is to find the closest classical state (CCS) for a given state ρ, which is in general a more complicated problem. In this work, we study three and four qubit graph-diagonal states and give the explicit expressions of CCS for these states. Using the CCS, we compute the quantum discord of graph-diagonal states of three and four qubit systems and show that there is a hierarchy for the quantum discord of graph-diagonal states of any three and four qubit systems. Then we classify the entanglement of graph-diagonal states of three and four qubit systems and draw the hierarchy of entanglement of these graph-diagonal states. Finally, we compare the hierarchy of quantum discord and quantum entanglement of the these graph-diagonal states and show that the hierarchy of quantum entanglement is at least in equivalence of quantum discord.

Graphical abstract

Keywords

Quantum Information 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Mohammad Ali Jafarizadeh
    • 1
  • Naser Karimi
    • 2
    Email author
  • Davood Amidi Sahlan
    • 1
  • Ahmad Heshmati
    • 3
  • Marziyeh Yahyavi
    • 1
  1. 1.Department of Theoretical Physics and AstrophysicsTabriz UniversityTabrizIran
  2. 2.Department of scienceFarhangian UniversityTehranIran
  3. 3.Department of PhysicsShabestar Branch, Islamic Azad UniversityShabestarIran

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