The European Physical Journal D

, Volume 50, Issue 1, pp 107–121 | Cite as

Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses

  • M. A. JafarizadehEmail author
  • M. Mahdian
  • A. Heshmati
  • K. Aghayar
Quantum Optics and Quantum Information


The three qubits mutually unbiased bases (MUB) diagonal density matrices with maximally entanglement in Greenberger-Horne-Zeilinger (GHZ) basis are studied. These are a natural generalization of Bell-state diagonal density matrices. The linearity of positive partial transpose (PPT) conditions allows one to specify completely PPT states or feasible region (FR) which form a polygon, where the projection of the feasible region to some two dimensional planes has lead to better visualization. To reveal the PPT entangled regions of these density matrices, we manipulate some appropriate optimal non-decomposable linear entanglement witnesses (EWs) as the envelope of family of linear optimal non-decomposable EWs. These nonlinear EWs are nonlinear functional of MUB diagonal states, so that they are nonnegative valued over all separable, but they are negative valued over some PPT entangled MUB diagonal states. Even though, these nonlinear EWs can not separate completely, the PPT entanglement region from separable one, but however in special cases they lead to necessary and sufficient condition for separability. To support the evidence, we study three categories for special choices of parameters in density matrices, and using the nonlinear EWs we can distinguish the region of PPT entangled states and separable states, completely. At the end some numerical simulations are provided to show the practical applicability of these nonlinear EWs in detecting some PPT entangled MUB diagonal states.


03.67.Mn Entanglement measures, witnesses, and other characterizations 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell’s inequalities, GHZ states, etc.) 


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Copyright information

© Springer 2008

Authors and Affiliations

  • M. A. Jafarizadeh
    • 1
    • 2
    • 3
    Email author
  • M. Mahdian
    • 1
  • A. Heshmati
    • 1
  • K. Aghayar
    • 1
  1. 1.Department of Theoretical Physics and AstrophysicsUniversity of TabrizTabrizIran
  2. 2.Institute for Studies in Theoretical Physics and MathematicsTehranIran
  3. 3.Research Institute for Fundamental SciencesTabrizIran

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