Quantum Information Processing

, Volume 13, Issue 2, pp 283–297 | Cite as

Super-quantum correlation and geometry for Bell-diagonal states with weak measurements

  • Yao-Kun Wang
  • Teng Ma
  • Heng Fan
  • Shao-Ming Fei
  • Zhi-Xi WangEmail author


We propose “weak one-way deficit” by weak measurements as the generalization of one-way deficit defined for standard projective measurements. The weak one-way deficit for Werner state is obtained analytically. We find that weak one-way deficit is smaller than the standard one-way deficit, which contrasts with a straightforward expectation based on the known fact that super-quantum discord by weak measurement is always larger than the quantum discord defined by projective measurement. On the other hand, by tuning the weak measurement continuously to the projective measurement, both weak one-way deficit and super-quantum discord converge to the same value, which is either the one-way deficit or the quantum discord both quantifying quantum correlation. In this sense, weak measurement does not necessarily capture more quantumness of correlations. We also give the geometry of super-quantum discord of the Bell-diagonal states with explicit geometrical figures. As an application, the dynamic behavior of super-quantum correlation including super-quantum discord and weak one-way deficit under decoherence is investigated. We find that the order relation of the super-quantum correlation and the quantum correlation remained unchanged under the phase flipping channel for the Bell-diagonal states and the Werner states.


Weak measurement Weak one-way deficit Super-quantum correlation 



This work was supported by the NSFC11275131 and KZ201210028032.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Yao-Kun Wang
    • 1
    • 2
  • Teng Ma
    • 1
  • Heng Fan
    • 3
  • Shao-Ming Fei
    • 1
    • 4
  • Zhi-Xi Wang
    • 1
    Email author
  1. 1.School of Mathematical SciencesCapital Normal UniversityBeijing China
  2. 2.College of MathematicsTonghua Normal UniversityTonghua China
  3. 3.Institute of PhysicsChinese Academy of SciencesBeijing China
  4. 4.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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