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International Journal of Theoretical Physics

, Volume 56, Issue 11, pp 3425–3430 | Cite as

Unextendible Maximally Entangled Bases and Mutually Unbiased Bases in Multipartite Systems

  • Ya-Jing Zhang
  • Hui ZhaoEmail author
  • Naihuan Jing
  • Shao-Ming Fei
Article

Abstract

We generalize the notion of unextendible maximally entangled basis from bipartite systems to multipartite quantum systems. It is proved that there do not exist unextendible maximally entangled bases in three-qubit systems. Moreover, two types of unextendible maximally entangled bases are constructed in tripartite quantum systems and proved to be not mutually unbiased.

Keywords

Unextendible maximally entangled bases Mutually unbiased bases Multipartite quantum systems 

Notes

Acknowledgements

This work supported by the National Natural Science Foundation of China grant Nos. 11675113, 11281137, 11271138, 11101017 and 11531004 and Simons Foundation grant No.198129.

References

  1. 1.
    Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Phys. Rev. Lett. 70, 1895 (1895)CrossRefGoogle Scholar
  2. 2.
    Fuchs, C.A., Gisin, N., Griffiths, R.B., Niu, C.S., Peres, A.: Phys. Rev. A 56, 1163 (1997)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Bennett, C.H., Wiesner, S.J.: Phys. Rev. Lett. 69, 2881 (1992)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    DiVincenzo, D.P.: Quantum computation. Science 270(5234), 255–261 (1995)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    DiVincenzo, D.P., Mor, T., Shor, P.W., Smolin, J.A., Terhal, B.M.: Comm. Math. Phys. 238, 379 (2003)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bennett, C.H., DiVincenzo, D.P., Mor, T., Shor, P.W., Smolin, J.A., Terhal, B.M.: Phys. Rev. Lett. 82, 5385 (1999)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Terhal, B.M.: Lin. Alg. Appl. 323(1), 61–73 (2000)MathSciNetGoogle Scholar
  8. 8.
    Pittenger, A.O.: Lin. Alg. Appl. 359, 235–248 (2003)CrossRefGoogle Scholar
  9. 9.
    Augusiak, R., Stasińska, J., Hadley, C., Korbicz, J.K., Lewenstein, M., Acín, A.: Phys. Rev. Lett. 107, 070401 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    Bravyi, S., Smolin, J.A.: Phys. Rev. A 84, 042306 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    Chen, B., Fei, S.M.: Phys. Rev. A 88, 034301 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    Li, M.S., Wang, Y.L., Zheng, Z.J.: Phys. Rev. A 89, 062313 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Guo, Y.: Phys. Rev. A 94, 052302 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    Guo, Y., Wu, S.: Phys. Rev. A 90, 054303 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    Guo, Y., Jia, Y., Li, X.: Quantum Inf. Process 14, 3553 (2015)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Wootters, W.K., Fields, B.D.: Ann. Phys. 191, 363 (1989)ADSCrossRefGoogle Scholar
  17. 17.
    Facchi, P., Florio, G., Parisi, G., Pascazio, S.: Phys. Rev. A 77, 060304 (2008)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Huber, F., Gühne, O., Siewert, J.: Phys. Rev. Lett. 118, 200502 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    Acín, A., Andrianov, A., Costa, L., Jané, E., Latorre, J.I., Tarrach, R.: Phys. Rev. Lett. 85, 1560 (2000)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Ya-Jing Zhang
    • 1
  • Hui Zhao
    • 1
    Email author
  • Naihuan Jing
    • 2
    • 3
  • Shao-Ming Fei
    • 4
  1. 1.College of Applied SciencesBeijing University of TechnologyBeijingChina
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of MathematicsShanghai UniversityShanghaiChina
  4. 4.School of Mathematical SciencesCapital Normal UniversityBeijingChina

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