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Distribution of entanglement in multipartite systems

  • Awais Khan
  • Ahmad Farooq
  • Youngmin JeongEmail author
  • Hyundong ShinEmail author
Article
  • 101 Downloads

Abstract

Distribution of entanglement for the multipartite systems is characterized through monogamy and polygamy relations. In this paper, we study the xth power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations based on the nonnegative power of Tsallis-q entanglement are obtained for N-qubit states and are shown to be tighter than existing relation. We find that for any tripartite mixed state, the Tsallis-q entanglement follows a polygamy relation. This polygamy relation also holds for the multi-qubit systems. The polygamy relations of the Tsallis-q entanglement, that are uniquely defined for generalized multi-qubit W-class states, and partially coherent superposition states are also examined. Moreover, the tighter monogamy bounds for concurrence of assistance and negativity of assistance are also established for these states, which gives more accurate bounds than existing relations.

Keywords

Concurrence Monogamy relations Polygamy relations Negativity Tsallis-q entanglement W-class state PCS states 

Notes

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2016R1A2B2014462), by the Basic Science Research Program through the NRF funded by the Ministry of Education (No. 2018R1D1A1B07050584), and ICT R&D program of MSIP/IITP [R0190-15-2030, Reliable crypto-system standards and core technology development for secure quantum key distribution network].

References

  1. 1.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Qaisar, S., Rehman, J.U., Jeong, Y., Shin, H.: Practical deterministic secure quantum communication in a lossy channel. Prog Theor Exp Phys 2017(4), 041A01 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Kumar, A., Roy, S.S., Pal, A.K., Prabhu, R., De, A.S., Sen, U.: Conclusive identification of quantum channels via monogamy of quantum correlations. Phys. Rev. A 380(43), 3588–3594 (2016)MathSciNetGoogle Scholar
  4. 4.
    Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000)ADSCrossRefGoogle Scholar
  5. 5.
    Osborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96(22), 220503 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    de Oliveira, T.R., Cornelio, M.F., Fanchini, F.F.: Monogamy of entanglement of formation. Phys. Rev. A 89(3), 034303 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    Ou, Y.C., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phys. Rev. A 75(6), 062308 (2007)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Kim, J.S., Das, A., Sanders, B.C.: Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity. Phys. Rev. A 79(1), 012329 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    Kim, J.S.: Tsallis entropy and entanglement constraints in multiqubit systems. Phys. Rev. A 81(6), 062328 (2010)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Luo, Y., Tian, T., Shao, L.H., Li, Y.: General monogamy of Tsallis \(q\)-entropy entanglement in multiqubit systems. Phys. Rev. A 93(6), 062340 (2016)ADSGoogle Scholar
  11. 11.
    Kim, J.S., Sanders, B.C.: Monogamy of multi-qubit entanglement using Rényi entropy. J. Phys. A: Math. Theor. 43(44), 445305 (2010)zbMATHCrossRefGoogle Scholar
  12. 12.
    Kim, J.S., Sanders, B.C.: Unified entropy, entanglement measures and monogamy of multi-party entanglement. J. Phys. A: Math. Theor. 44(29), 295303 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Gour, G., Bandyopadhyay, S., Sanders, B.C.: Dual monogamy inequality for entanglement. J. Math. Phys. 48(1), 012108 (2007)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Buscemi, F., Gour, G., Kim, J.S.: Polygamy of distributed entanglement. Phys. Rev. A 80, 012324 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    Kim, J.S., Sanders, B.C.: Generalized W-class state and its monogamy relation. J. Phys. A: Math. Theor. 41(49), 495301 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Kim, J.S.: Strong monogamy of quantum entanglement for multiqubit W-class states. Phys. Rev. A 90(6), 062306 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    Kim, J.S.: Strong monogamy of multiparty quantum entanglement for partially coherently superposed states. Phys. Rev. A 93(3), 032331 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    Zhu, X.N., Fei, S.M.: General monogamy relations of quantum entanglement for multiqubit W-class states. Quantum Inf. Process. 16(2), 53 (2017)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Jin, Z.X., Fei, S.M.: Tighter monogamy relations of quantum entanglement for multiqubit W-class states. Quantum Inf. Process. 17(1), 2 (2018)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Uhlmann, A.: Fidelity and concurrence of conjugated states. Phys. Rev. A 62(3), 032307 (2000)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Lee, S., Chi, D.P., Oh, S.D., Kim, J.: Convex-roof extended negativity as an entanglement measure for bipartite quantum systems. Phys. Rev. A 68(6), 062304 (2003)ADSCrossRefGoogle Scholar
  22. 22.
    Horodecki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232(3), 333–339 (1997)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Dür, W., Cirac, J., Lewenstein, M., Bruß, D.: Distillability and partial transposition in bipartite systems. Phys. Rev. A 61(6), 062313 (2000)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Audenaert, K.M.: Subadditivity of \(q\)-entropies for q \(\ge 1\). J. Math. Phys. 48(8), 083507 (2007)ADSMathSciNetzbMATHGoogle Scholar
  25. 25.
    Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74(6), 062320 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    shui Yu, C., shan Song, H.: Measurable entanglement for tripartite quantum pure states of qubits. Phys. Rev. A 76(2), 022324 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    Jin, Z.X., Li, J., Li, T., Fei, S.M.: Tighter monogamy relations in multiqubit systems. Phys. Rev. A 97(3), 032336 (2018)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86(5), 910 (2001)ADSCrossRefGoogle Scholar
  29. 29.
    Humphreys, P.C., Barbieri, M., Datta, A., Walmsley, I.A.: Quantum enhanced multiple phase estimation. Phys. Rev. Lett. 111(7), 070403 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    Liu, J., Lu, X.M., Sun, Z., Wang, X.: Quantum multiparameter metrology with generalized entangled coherent state. J. Phys. A: Math. Theor. 49(11), 115302 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Electronic EngineeringKyung Hee UniversityYongin-siKorea

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