Advertisement

Quantum Discord of Certain Two-Qubit States

  • Jianming Zhou
  • Xiaoli HuEmail author
  • Naihuan Jing
Article

Abstract

Quantum discord is an effective measure of quantum correlation introduced by Olliver and Zurek. We evaluate analytically the quantum discord for a large family of non-X-states. Exact solutions of the quantum discord are obtained for four parametric spaces of non-X-states. Dynamic behavior of the quantum discord is also explored under the action of the Kraus operator.

Keywords

Quantum discord Quantum correlations Bipartite quantum states Optimization on manifolds 

Notes

Acknowledgments

The corresponding author gratefully acknowledges the partial support of NSFC grants 11426116, 11501251 and 11871325 during this work. The third author is supported by NSFC grant 11531004 and Simons Foundation grant 523868.

References

  1. 1.
    Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: . Rev. Mod. Phys. 84, 1655 (2012)ADSCrossRefGoogle Scholar
  2. 2.
    Streltsov, A.: Quantum Correlations beyond Entanglement and Their Role in Quantum Information Theory. SpringerBriefs in Physics. Springer, Berlin (2015)zbMATHGoogle Scholar
  3. 3.
    Adesso, G., Bromiey, T.R., Cianciaruso, M.: . J. Phys. A: Math. Theor. 49, 473001 (2016)ADSCrossRefGoogle Scholar
  4. 4.
    Sabapathy, K.K., Simon, R.: arXiv:1311.0210v1
  5. 5.
    Yurischev, M.A.: . Quantum Inf. Process. 14, 3399 (2015)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Li, B., Wang, Z.X., Fei, S.M.: . Phys. Rev. A 83, 022321 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Ollivier, H., Zurek, W.H.: . Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefGoogle Scholar
  8. 8.
    Dakíc, B., Vedral, V., Brukner, Č.: . Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    Ali, M., Rau, A.R.P., Alber, G.: . Phys. Rev. A 81, 042105 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Girolami, D., Adesso, G.: . Phys. Rev. A 83, 052108 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Galve, F., Giorgi, G., Zambrini, R.: . Europhys. Lett. 96, 40005 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Chen, Q., Zhang, C., Yu, S., Yi, X.-X., Oh, C.-H.: . Phys. Rev. A 84, 042313 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: . Phys. Rev. A 81, 052107 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    Huang, Y.: . Phys. Rev. A 88, 014302 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    Vedral, V.: . Rev. Mod. Phys. 74, 197 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    Groisman, B., Popescu, S., Winter, A.: . Phy. Rev. A 72, 032317 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    Schumacher, B., Westmoreland, M.D.: . Phys. Rev. A 74, 042305 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    Li, N., Luo, S.: . Phys. Rev. A 76, 032327 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    Streltsov, A.: Quantum correlations beyond entanglement. Springer Briefs in Physics Springer International Publishing (2015)Google Scholar
  20. 20.
    Long, S.: . Phys. Rev. A 77, 042303 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Jing, N., Yu, B.: . J. Phys. A: Math. Theor. 49, 385302 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: . Phys. Rev. A 80, 024103 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    Fanchini, F.F., Werlang, T., Brasil, C.A., Arruda, L.G.E., Caldeira, A.O.: . Phys. Rev. A 81, 052107 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Ye, B.-L., Wang, Y.-K., Fei, S.-M.: . Int. J. Theor. Phys. 55, 2237 (2016)CrossRefGoogle Scholar
  25. 25.
    Zhu, X.-N., Fei, S.-M., Li-Jost X.-Q.: . Quantum inf. Process. 17, 234 (2018)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceJianghan UniversityWuhanChina
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA

Personalised recommendations