, 91:45 | Cite as

Detecting identical entanglement pure states for two qubits

  • Wei Deng
  • Yong DengEmail author


Entanglement is one of the most surprising features of composite quantum systems. Yet, challenges remain in our understanding and quantification of the entanglement. There is no unique degree of entanglement from various measures, as presented by numerous studies on quantifying entanglement. As indicated in this paper, any degree of entanglement for two qubits resulting from a particular measure can be detected in excess of one corresponding pure state. Evidently, those identical entanglement pure states can be counted as a quantitative condition to be satisfied by other proper measures. The most popular measures of pure states for two qubits are based on the same structure, as indicated in this paper. Then, the algorithm to detect the identical entanglement pure states for two qubits is proposed based on randomness distillation. Eventually, two sets of identical entanglement states are listed for two qubits.


Identical entanglement detection randomness distillation. 


03.65.Ud 05.70.–a 02.50.–r 



The authors greatly appreciate the reviewers’ suggestions and the editor’s encouragement. The work was partially supported by the National Natural Science Foundation of China (Grant Nos 61573290 and 61503237).


  1. 1.
    E. Schrödinger, Naturwissenschaften 23(823), 807 (1935)ADSCrossRefGoogle Scholar
  2. 2.
    S Abdel-Khalek, Y S El-Saman and M Abdel-Aty, Pramana – J. Phys. 90(1): 1 (2018)ADSCrossRefGoogle Scholar
  3. 3.
    F Ozaydin, Quantum pseudo-telepathy in spin systems: Magic square game under magnetic fields and Dzyaloshinskii–Moriya interaction, arXiv preprint arXiv:1609.03881 (2016)
  4. 4.
    X Zong-Cheng, L Mai-Lin, Z Ya-Ting and Y Jian-Quan, Pramana – J. Phys. 86(3), 495 (2016)ADSCrossRefGoogle Scholar
  5. 5.
    N Nayak, B Ghosh and A S Majumdar, Indian J. Phys. 84(8), 1039 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    V Erol, F Ozaydin and A A Altintas, Sci. Rep. 4, 5422 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    E K Bashkirov and M S Mastyugin, Pramana – J. Phys. 84(1), 127 (2015)ADSCrossRefGoogle Scholar
  8. 8.
    V Vedral, Nature 453(7198), 1004 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    R Horodecki, P Horodecki, M Horodecki and K Horodecki, Rev. Mod. Phys. 81(2), 865 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    C B Dağ, W Niedenzu, Ö E Müstecaplıoğlu and G Kurizki. Entropy 18(7), 244 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    A K Maurya, M K Mishra and H Prakash, Pramana – J. Phys. 86(3), 515 (2016)Google Scholar
  12. 12.
    M B Plbnio and S Virmani, Quantum Inf. Comput. 7(1), 1 (2005)Google Scholar
  13. 13.
    C Eltschka and J Siewert, J. Phys. A: Math. Theor. 47(42), 424005 (2014)ADSCrossRefGoogle Scholar
  14. 14.
    G Adesso, T R Bromley and M Cianciaruso, J. Phys. A: Math. Theor. 49, 473001 (2016)Google Scholar
  15. 15.
    S Khan and N A Khan Pramana – J. Phys. 87(4), 61 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    S Luo, Lett. Math. Phys. 53(3), 243 (2000)MathSciNetCrossRefGoogle Scholar
  17. 17.
    F Ozaydin, A Ali Altintas, C Yesilyurt, S Bugu and V Erol, Acta Phys. Pol. A 127(4), 1233 (2015)Google Scholar
  18. 18.
    F Ozaydin, A A Altintas, S Bugu and C Yesilyurt, Int. J. Theor. Phys. 52(9), 2977 (2013)CrossRefGoogle Scholar
  19. 19.
    S Abdel-Khalek and S H A Halawani, Pramana – J. Phys. 85(6), 1089 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    J Eisert and M B Plenio, J. Mod. Opt. 46(1), 145 (1999)ADSCrossRefGoogle Scholar
  21. 21.
    F Verstraete, K Audenaert, J Dehaene and B De Moor, J. Phys. A: Math. Gen. 34(47), 10327 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    A Miranowicz and A Grudka, J. Opt. B: Quantum Semiclass. Opt. 6(12), 542 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    D Das, R Sengupta and Aravind, Pramana – J. Phys. 88(6): 82 (2017)Google Scholar
  24. 24.
    X Zhou, Y Hu, Y Deng, F T S Chan and A Ishizaka, Ann. Oper. Res. (2018)
  25. 25.
    R Zhang, B Ashuri and Y Deng, Adv. Data Anal. Class. 11(4), 759 (2017)CrossRefGoogle Scholar
  26. 26.
    H Xu and Y Deng, IEEE Access 6, 11634 (2018)CrossRefGoogle Scholar
  27. 27.
    X Deng and Y Deng, Soft Comput., published online, (2018)
  28. 28.
    B Kang, G Chhipi-Shrestha, Y Deng, K Hewage and R Sadiq, Appl. Math. Comput. 324, 202 (2018)MathSciNetGoogle Scholar
  29. 29.
    Q Zhang, M Li and Y Deng, Phys. A: Stat. Mech. Appl. 491, 749 (2018)CrossRefGoogle Scholar
  30. 30.
    X Zheng and Y Deng, Ann. Nucl. Energy 112, 673 (2018)CrossRefGoogle Scholar
  31. 31.
    J Eisert and H J Briegel, Phys. Rev. A 64(2), 022306 (2001)ADSCrossRefGoogle Scholar
  32. 32.
    J Sperling and W Vogel, Phys. Scr. 83(4), 045002 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    P Vivo, M P Pato and G Oshanin, Phys. Rev. E 93(5), 052106 (2016)ADSCrossRefGoogle Scholar
  34. 34.
    A F Abouraddy, B E A Saleh, A V Sergienko and M C Teich, Phys. Rev. A 64(5), 050101 (2001)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    S Hill and W K Wootters, Phys. Rev. Lett. 78(26), 5022 (1997)ADSCrossRefGoogle Scholar
  36. 36.
    V Vedral, M B Plenio, M A Rippin and P L Knight, Phys. Rev. Lett. 78(12), 2275 (1997)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    M A Nielsen and I L Chuang, Quantum computation and quantum information (Cambridge University Press, Cambridge, 2010)Google Scholar
  38. 38.
    G Sentís, C Eltschka, O Gühne, M Huber and J Siewert, Phys. Rev. Lett. 117(9), 190502 (2016)ADSCrossRefGoogle Scholar
  39. 39.
    H Di Lorenzo Pires, C H Monken and M P van Exter, Phys. Rev. A 80(2), 022307 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    V Vedral and M B Plenio, Phys. Rev. A 57(3), 1619 (1998)ADSCrossRefGoogle Scholar
  41. 41.
    A Shimony, Ann. NY Acad. Sci. 755(1), 675 (1995)ADSCrossRefGoogle Scholar
  42. 42.
    M A Horne, A Shimony and A Zeilinger, Phys. Rev. Lett. 62(19), 2209 (1989)ADSCrossRefGoogle Scholar
  43. 43.
    J-L Chen, L Fu, A A Ungar and X-G Zhao, Phys. Rev. A 65(4), 044303 (2002)ADSCrossRefGoogle Scholar
  44. 44.
    M B Plenio, Phys. Rev. Lett. 95(9), 090503 (2005)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    M Horodecki, P Horodecki and R Horodecki, Phys. Rev. A 60(3), 1888 (1999)ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    K G H Vollbrecht and M M Wolf, J. Math. Phys. 43(9), 4299 (2002)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    L Henderson and V Vedral, Phys. Rev. Lett. 84(10), 2263 (2000)ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.School of Computer and Information ScienceSouthwest UniversityChongqing People’s Republic of China

Personalised recommendations