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Tighter Constraints of Quantum Correlations Among Multipartite Systems

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Abstract

We provide a characterization of multipartite systems constraints in terms of quantum correlations. By using the Hamming weight of the binary vectors associated with the subsystems, we give the α th power of monogamy and β th power of polygamy inequalities for general quantum correlations. Using concurrence as an application, one gets tighter inequalities than the existing ones for some classes of quantum states. Detailed examples are presented.

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References

  1. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. CambridgeUniversity Press, Cambridge(2000). Press (2000)

    MATH  Google Scholar 

  2. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Mintert, F., Kuś, M., Buchleitner, A.: Concurrence of mixed bipartite quantum states in arbitrary dimensions. Phys. Rev. Lett. 92, 167902 (2004)

    Article  ADS  Google Scholar 

  4. Chen, K., Albeverio, S., Fei, S.M.: Concurrence of arbitrary dimensional bipartite quantum states. Phys. Rev. Lett. 95, 040504 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  5. Breuer, H.P.: Separability criteria and bounds for entanglement measures. J. Phys A Math. Gen. 39, 11847 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Breuer, H.P.: Optimal entanglement criterion for mixed quantum states. Phys. Rev. Lett. 97, 080501 (2006)

    Article  ADS  Google Scholar 

  7. de Vicente, J.I.: Lower bounds on concurrence and separability conditions. Phys. Rev. A 75, 052320 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  8. Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Optimal entanglement witnesses based on local orthogonal observables. Phys. Rev. A 76, 012334 (2007)

    Article  ADS  Google Scholar 

  9. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Pawlowski, M.: Security proof for cryptographic protocols based only on the monogamy of bells inequality violations. Phys. Rev. A 82, 032313 (2010)

    Article  ADS  Google Scholar 

  12. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)

    Article  ADS  Google Scholar 

  13. Raussendorf, R., Briegel, H.J.: A One-Way quantum computer. Phys. Rev. Lett. 86, 5188 (2001)

    Article  ADS  Google Scholar 

  14. Koashi, M., Winter, A.: Monogamy of quantum entanglement and other correlations. Phys. Rev. A 69, 022309 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  15. Osborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006)

    Article  ADS  Google Scholar 

  16. Jin, Z.X., Fei, S.M.: Tighter monogamy relations of quantum entanglement for multiqubit W-class states. Quantum Inf Process 17, 2 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Bai, Y.K., Ye, M.Y., Wang, Z.D.: Entanglement monogamy and entanglement evolution in multipartite systems. Phys. Rev. A 80, 044301 (2009)

    Article  ADS  Google Scholar 

  18. de Oliveira, T.R., Cornelio, M.F., Fanchini, F.F.: Monogamy of entanglement of formation. Phys. Rev. A 89, 034303 (2014)

    Article  ADS  Google Scholar 

  19. Adesso, G., Illuminati, F.: Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems. New J. Phys. 8, 15 (2006)

    Article  ADS  Google Scholar 

  20. Hiroshima, T., Adesso, G., Illuminati, F.: Monogamy inequality for distributed gaussian entanglement. Phys. Rev. Lett. 98, 050503 (2007)

    Article  ADS  Google Scholar 

  21. Adesso, G., Illuminati, F.: Strong monogamy of bipartite and genuine multiparitie entanglement: The gaussian case. Phys. Rev. Lett. 99, 150501 (2007)

    Article  ADS  Google Scholar 

  22. Christandl, M., Winter, A.: Squashed entanglement: An additive entanglement measure. J. Math. Phys. 45, 829 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Yang, D., et al.: Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof. IEEE Trans. Inf. Theory 55, 3375 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ou, Y.C., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phys. Rev. A 75, 062308 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  25. Jin, Z.X., Li, J., Li, T., Fei, S.M.: Tighter monogamy relations in multiqubit systems. Phys. Rev. A 97, 032336 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  26. Jin, Z.X., Fei, S.M.: Superactivation of monogamy relations for nonadditive quantum correlation measures. Phys. Rev. A 99, 032343 (2019)

    Article  ADS  Google Scholar 

  27. Kim, J.S., Das, A., Sanders, B.C.: Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extend negativity. Phys. Rev. A 79, 012329 (2009)

    Article  ADS  Google Scholar 

  28. He, H., Vidal, G.: Disentangling theorem and monogamy for entanglement negativity. Phys. Rev. A 91, 012339 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  29. Choi, J.H., Kim, J.S.: Negativity and strong monogamy of multiparty quantum entanglement beyond qubits. Phys. Rev. A 92, 042307 (2015)

    Article  ADS  Google Scholar 

  30. Luo, Y., Li, Y.: Monogamy of α-th power entanglement measurement in qubit system. Ann. Phys. 362, 511 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Kim, J.S.: Tsallis entropy and entanglement constraints in multiqubit systems. Phys. Rev. A 81, 062328 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  32. Kim, J.S.: Generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Ann. Phys. 373, 197–206 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Kim, J.S., Sanders, B.C.: Monogamy of multi-qubit entanglement using rényi entropy. J. Phys. A Math. Theor. 43, 445305 (2010)

    Article  MATH  Google Scholar 

  34. Cornelio, M.F., de Oliveira, M.C.: Strong superadditivity and monogamy of the Renyi measure of entanglement. Phys. Rev. A 81, 032332 (2010)

    Article  ADS  Google Scholar 

  35. Wang, Y.X., Mu, L.Z., Vedral, V., Fan, H.: Entanglement rényi-entropy. Phys. Rev. A 93, 022324 (2016)

    Article  ADS  Google Scholar 

  36. Gour, G., Meyer, D.A., Sanders, B.C.: Deterministic entanglement of assistance and monogamy constraints. Phys. Rev. A 72, 042329 (2005)

    Article  ADS  Google Scholar 

  37. Kim, J.S.: Tsallis entropy and entanglement constraints in multiqubit systems. Phys. Rev. A 81, 062328 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  38. Jin, Z.X., Qiao, C.-F.: Monogamy and polygamy relations of multiqubit entanglement based on unified entropy. Chin. Phys. B 29, 020305 (2020)

    Article  ADS  Google Scholar 

  39. Goura, G., Bandyopadhyayb, S., Sandersc, B.C.: Dual monogamy inequality for entanglement. J. Math. Phys. 48, 012108 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  40. Jin, Z.X., Fei, S.M., Qiao, C.-F.: Complementary quantum correlations among multipartite systems. Quantum Inf Process 19, 101 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  41. Jin, Z.X., Fei, S.M.: Polygamy relations of multipartite entanglement beyond qubits. J. Phys. A Math. Theor. 52, 165303 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  42. Buscemi, F., Gour, G., Kim, J.S.: Polygamy of distributed entanglement. Phys. Rev. A 80, 012324 (2009)

    Article  ADS  Google Scholar 

  43. Kim, J.S.: General polygamy inequality of multiparty quantum entanglement. Phys. Rev. A 85, 062302 (2012)

    Article  ADS  Google Scholar 

  44. Kim, J.S.: Tsallis entropy and general polygamy of multiparty quantum entanglement in arbitrary dimensions,. Phys. Rev. A 94, 062338 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  45. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  MATH  Google Scholar 

  46. Kumar, A., Prabhu, R., Sen(de), A., Sen, U.: Effect of a large number of parties on the monogamy of quantum correlations. Phys. Rev. A 91, 012341 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  47. Jin, Z.X., Fei, S.M.: Monogamy relations of all quantum correlation measures for multipartite quantum systems. Optics Commun. 446, 39–43 (2019)

    Article  ADS  Google Scholar 

  48. Salini, K., Prabhu, R., Sen(de), A., Sen, U.: Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous. Ann. Phys 348, 297–305 (2014)

    Article  ADS  MATH  Google Scholar 

  49. Laustsen, T., Verstraete, F., Van Enk, S.J.: Local vs. joint measurements for the entanglement of assistance. Quantum Inf. Comput. 3, 64 (2003)

    MathSciNet  MATH  Google Scholar 

  50. Yu, C.S., Song, H.S.: Entanglement monogamy of tripartite quantum states. Phys. Rev. A 77, 032329 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. Goura, G., Bandyopadhyayb, S., Sandersc, B.C.: Dual monogamy inequality for entanglement. J. Math. Phys. 48, 012108 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  52. Jin, Z.X., Fei, S.M.: Tighter entanglement monogamy relations of qubit systems. Quantum Inf Process 16, 77 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. Kim, J.S.: Negativity and tight constraints of multiqubit entanglement. Phys. Rev. A 97, 012334 (2018)

    Article  ADS  Google Scholar 

  54. Jin, Z.X., Fei, S.M.: Finer distribution of quantum correlations among multiqubit systems. Quantum Inf Process 18, 21 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Liu, D. Tighter Constraints of Quantum Correlations Among Multipartite Systems. Int J Theor Phys 60, 1455–1470 (2021). https://doi.org/10.1007/s10773-021-04770-8

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  • DOI: https://doi.org/10.1007/s10773-021-04770-8

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