Skip to main content
Log in

Tripartite quantum discord dynamics in qubits driven by the joint influence of distinct classical noises

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We investigate the dynamics of quantum discord in a system of three non-interacting qubits, initially entangled in a Greenberger–Horne–Zeilinger state, in the presence of mixed classical environments. Precisely, the joint impacts of a static noise (SN) and a random telegraphic noise (RTN) are probed, by combining them in two different ways: independent and bipartite system–environment coupling. For both cases, one marginal system is coupled with an environment (say \(E_1\)), and the remaining subsystems are coupled either locally or not with a second environment (\(E_2\)), and vice versa. We show that quantum discord is more fragile in independent environments than in bipartite ones no matter the Markovianity of the dynamical process, and may exhibit sudden death and revival phenomena. A static noise is more fatal to the survival of quantum discord than a RTN, and its shielding effects are more pronounced as the number of subsystems under its effects increases. The opposite is found for a RTN, where discord robustness is enhanced as the number of affected subsystems increases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Datta, A., Flammia, S.T., Caves, C.M.: Entanglement and the power of one qubit. Phys. Rev. A (2005). https://doi.org/10.1103/physreva.72.042316

    Article  Google Scholar 

  2. Datta, A., Vidal, G.: Role of entanglement and correlations in mixed-state quantum computation. Phys. Rev. A (2007). https://doi.org/10.1103/physreva.75.042310

    Article  MathSciNet  Google Scholar 

  3. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett (2008). https://doi.org/10.1103/physrevlett.100.050502

    Article  Google Scholar 

  4. Lanyon, B.P., Barbieri, M., Almeida, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. (2008). https://doi.org/10.1103/physrevlett.101.200501

    Article  Google Scholar 

  5. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)

    MATH  Google Scholar 

  6. Cui, J., Gu, M., Kwek, L.C., Santos, M.F., Fan, H., Vedral, V.: Quantum phases with differing computational power. Nat. Commun. (2012). https://doi.org/10.1038/ncomms1809

    Article  Google Scholar 

  7. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935). https://doi.org/10.1103/physrev.47.777

    Article  ADS  MATH  Google Scholar 

  8. Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81(25), 5672 (1998). https://doi.org/10.1103/physrevlett.81.5672

    Article  ADS  Google Scholar 

  9. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett (2001). https://doi.org/10.1103/physrevlett.88.017901

    Article  MATH  Google Scholar 

  10. Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34(35), 6899 (2001). https://doi.org/10.1088/0305-4470/34/35/315

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Vedral, V.: Classical correlations and entanglement in quantum measurements. Phys. Rev. Lett. (2003). https://doi.org/10.1103/physrevlett.90.050401

    Article  Google Scholar 

  12. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84(4), 1655 (2012). https://doi.org/10.1103/revmodphys.84.1655

    Article  ADS  Google Scholar 

  13. Datta, A., Shaji, A.: Quantum discord and quantum computing—an appraisal. Int. J. Quantum Inf. 9(07n08), 1787 (2011). https://doi.org/10.1142/s0219749911008416

    Article  MathSciNet  MATH  Google Scholar 

  14. Werlang, T., Trippe, C., Ribeiro, G.A.P., Rigolin, G.: Quantum correlations in spin chains at finite temperatures and quantum phase transitions. Phys. Rev. Lett. (2010). https://doi.org/10.1103/physrevlett.105.095702

    Article  Google Scholar 

  15. Dillenschneider, R.: Quantum discord and quantum phase transition in spin chains. Phys. Rev. B (2008). https://doi.org/10.1103/physrevb.78.224413

    Article  Google Scholar 

  16. Roa, L., Retamal, J.C., Alid-Vaccarezza, M.: Dissonance is required for assisted optimal state discrimination. Phys. Rev. Lett. 107, 080401 (2011). https://doi.org/10.1103/PhysRevLett.107.080401

    Article  ADS  Google Scholar 

  17. Li, B., Fei, S.M., Wang, Z.X., Fan, H.: Assisted state discrimination without entanglement. Phys. Rev. A (2012). https://doi.org/10.1103/physreva.85.022328

    Article  Google Scholar 

  18. Cui, J., Fan, H.: Correlations in the Grover search. J. Phys. A: Math. Theor. 43(4), 045305 (2010). https://doi.org/10.1088/1751-8113/43/4/045305

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Biham, E., Brassard, G., Kenigsberg, D., Mor, T.: Quantum computing without entanglement. Theoret. Comput. Sci. 320(1), 15 (2004). https://doi.org/10.1016/j.tcs.2004.03.041

    Article  MathSciNet  MATH  Google Scholar 

  20. Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. (2004). https://doi.org/10.1103/physrevlett.93.140404

    Article  Google Scholar 

  21. Yu, T., Eberly, J.: Sudden death of entanglement: classical noise effects. Opt. Commun. 264(2), 393 (2006). https://doi.org/10.1016/j.optcom.2006.01.061

    Article  ADS  Google Scholar 

  22. Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323(5914), 598 (2009). https://doi.org/10.1126/science.1167343

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Werlang, T., Souza, S., Fanchini, F.F., Boas, C.J.V.: Robustness of quantum discord to sudden death. Phys. Rev. A (2009). https://doi.org/10.1103/physreva.80.024103

    Article  Google Scholar 

  24. Yeo, Y., An, J.H., Oh, C.H.: Non-Markovian effects on quantum-communication protocols. Phys. Rev. A. (2010). https://doi.org/10.1103/physreva.82.032340

    Article  Google Scholar 

  25. Gu, M., Chrzanowski, H.M., Assad, S.M., Symul, T., Modi, K., Ralph, T.C., Vedral, V., Lam, P.K.: Observing the operational significance of discord consumption. Nat. Phys. 8(9), 671 (2012). https://doi.org/10.1038/nphys2376

    Article  Google Scholar 

  26. Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75(3), 715 (2003). https://doi.org/10.1103/revmodphys.75.715

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Metwally, N., Eleuch, H., Obada, A.S.: Sudden death and rebirth of entanglement for different dimensional systems driven by a classical random external field. Laser Phys. Lett. 13(10), 105206 (2016). https://doi.org/10.1088/1612-2011/13/10/105206

    Article  ADS  Google Scholar 

  28. Bellomo, B., Franco, R.L., Maniscalco, S., Compagno, G.: Entanglement trapping in structured environments. Phys. Rev. A (2008). https://doi.org/10.1103/physreva.78.060302

    Article  Google Scholar 

  29. An, N.B., Kim, J., Kim, K.: Entanglement dynamics of three interacting two-level atoms within a common structured environment. Phys. Rev. A (2011). https://doi.org/10.1103/physreva.84.022329

    Article  Google Scholar 

  30. Buscemi, F., Bordone, P., Bertoni, A.: Validity of the single-particle approach for electron transport in quantum wires assisted by surface acoustic waves. J. Phys. Condens. Matter 21(30), 305303 (2009). https://doi.org/10.1088/0953-8984/21/30/305303

    Article  Google Scholar 

  31. Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.: Effects of classical environmental noise on entanglement and quantum discord dynamics. Int. J. Quantum Inf. 10(08), 1241005 (2012). https://doi.org/10.1142/s0219749912410055

    Article  MathSciNet  MATH  Google Scholar 

  32. Benedetti, C., Paris, M.G.A., Buscemi, F., Bordone, P.: Time-evolution of entanglement and quantum discord of bipartite systems subject to \(1/f^{\alpha }\) noise. In: 2013 22nd International Conference on Noise and Fluctuations (ICNF) IEEE (2013). https://doi.org/10.1109/icnf.2013.6578952

  33. Leggio, B., Franco, R.L., Soares-Pinto, D.O., Horodecki, P., Compagno, G.: Distributed correlations and information flows within a hybrid multipartite quantum-classical system. Phys. Rev. A (2015). https://doi.org/10.1103/physreva.92.032311

    Article  Google Scholar 

  34. D’Arrigo, A., Benenti, G., Franco, R.L., Falci, G., Paladino, E.: Hidden entanglement, system-environment information flow and non-Markovianity. Int. J. Quantum Inf. 12(02), 1461005 (2014). https://doi.org/10.1142/s021974991461005x

    Article  MathSciNet  MATH  Google Scholar 

  35. Xu, J.S., Sun, K., Li, C.F., Xu, X.Y., Guo, G.C., Andersson, E., Franco, R.L., Compagno, G.: Experimental recovery of quantum correlations in absence of system-environment back-action. Nat. Commun. (2013). https://doi.org/10.1038/ncomms3851

    Article  Google Scholar 

  36. Orieux, A., D’Arrigo, A., Ferranti, G., Franco, R.L., Benenti, G., Paladino, E., Falci, G., Sciarrino, F., Mataloni, P.: Experimental on-demand recovery of entanglement by local operations within non-Markovian dynamics. Sci. Rep. (2015). https://doi.org/10.1038/srep08575

    Article  Google Scholar 

  37. Arthur, T.T., Martin, T., Fai, L.C.: Disentanglement and quantum states transitions dynamics in spin-qutrit systems: dephasing random telegraph noise and the relevance of the initial state. Quantum Inf. Process. (2018). https://doi.org/10.1007/s11128-017-1800-y

    Article  MathSciNet  MATH  Google Scholar 

  38. Buscemi, F., Bordone, P.: Time evolution of tripartite quantum discord and entanglement under local and nonlocal random telegraph noise. Phys. Rev. A (2013). https://doi.org/10.1103/physreva.87.042310

    Article  Google Scholar 

  39. Kim, K.I., Li, H.M., Zhao, B.K.: Genuine tripartite entanglement dynamics and transfer in a triple Jaynes-Cummings model. Int. J. Theor. Phys. 55(1), 241 (2015). https://doi.org/10.1007/s10773-015-2656-5

    Article  MATH  Google Scholar 

  40. Espoukeh, P., Rahimi, R., Salimi, S., Pedram, P.: Dynamics of entanglement and non-classical correlation for four-qubit GHZ state. Int. J. Quantum Inf. 13(06), 1550044 (2015). https://doi.org/10.1142/s0219749915500446

    Article  MathSciNet  MATH  Google Scholar 

  41. Sadiek, G., Almalki, S.: Entanglement dynamics in Heisenberg spin chains coupled to a dissipative environment at finite temperature. Phys. Rev. A (2016). https://doi.org/10.1103/physreva.94.012341

    Article  Google Scholar 

  42. Tchoffo, M., Kenfack, L.T., Fouokeng, G.C., Fai, L.C.: Quantum correlations dynamics and decoherence of a three-qubit system subject to classical environmental noise. Euro. Phys. J. Plus (2016). https://doi.org/10.1140/epjp/i2016-16380-3

    Article  Google Scholar 

  43. Park, D.: Tripartite entanglement dynamics in the presence of Markovian or non-Markovian environment. Quantum Inf. Process. 15(8), 3189 (2016). https://doi.org/10.1007/s11128-016-1331-y

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. Kenfack, L.T., Tchoffo, M., Fai, L.C., Fouokeng, G.C.: Decoherence and tripartite entanglement dynamics in the presence of Gaussian and non-Gaussian classical noise. Physica B 511, 123 (2017). https://doi.org/10.1016/j.physb.2017.02.011

    Article  ADS  Google Scholar 

  45. Kenfack, L.T., Tchoffo, M., Fai, L.C.: Dynamics of tripartite quantum entanglement and discord under a classical dephasing random telegraph noise. Euro. Phys. J. Plus 132(2), 91 (2017). https://doi.org/10.1140/epjp/i2017-11364-5

    Article  Google Scholar 

  46. Arthur, T.T., Martin, T., Fai, L.C.: Dynamics of tripartite quantum correlations and decoherence in flux qubit systems under local and non-local static noise. Quantum Inf. Process (2018). https://doi.org/10.1007/s11128-018-1899-5

    Article  MathSciNet  MATH  Google Scholar 

  47. Tchoffo, M., Tsokeng, A.T., Tiokang, O.M., Nganyo, P.N., Fai, L.C.: Frozen entanglement and quantum correlations of one-parameter qubit-qutrit states under classical noise effects. Phys. Lett. A 383(16), 1856 (2019). https://doi.org/10.1016/j.physleta.2019.03.022

    Article  ADS  Google Scholar 

  48. Kenfack, L.T., Tchoffo, M., Javed, M., Fai, L.C.: Dynamics and protection of quantum correlations in a qubit-qutrit system subjected locally to a classical random field and colored noise. Quantum Inf. Process (2020). https://doi.org/10.1007/s11128-020-2599-5

    Article  MathSciNet  Google Scholar 

  49. Wang, B., Xu, Z.Y., Chen, Z.Q., Feng, M.: Non-Markovian effect on the quantum discord. Phys. Rev. A (2010). https://doi.org/10.1103/physreva.81.014101

    Article  Google Scholar 

  50. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A (2008). https://doi.org/10.1103/physreva.77.042303

    Article  Google Scholar 

  51. Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubitXstates. Phys. Rev. A (2010). https://doi.org/10.1103/physreva.81.042105

    Article  Google Scholar 

  52. Sarandy, M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A (2009). https://doi.org/10.1103/physreva.80.022108

    Article  Google Scholar 

  53. Giorgi, G.L., Bellomo, B., Galve, F., Zambrini, R.: Genuine Quantum and Classical Correlations in Multipartite Systems. Phys. Rev. Lett. (2011). https://doi.org/10.1103/physrevlett.107.190501

    Article  Google Scholar 

  54. Zhao, L., Hu, X., Yue, R.H., Fan, H.: Genuine correlations of tripartite system. Quantum Inf. Process. 12(7), 2371 (2013). https://doi.org/10.1007/s11128-013-0525-9

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. Beggi, A., Buscemi, F., Bordone, P.: Analytical expression of genuine tripartite quantum discord for symmetrical X-states. Quantum Inf. Process. 14(2), 573 (2014). https://doi.org/10.1007/s11128-014-0882-z

    Article  ADS  MathSciNet  MATH  Google Scholar 

  56. Falaye, B.J., Sun, G.H., Camacho-Nieto, O., Dong, S.H.: JRSP of three-particle state via three tripartite GHZ class in quantum noisy channels. Int. J. Quantum Inf. 14(07), 1650034 (2016). https://doi.org/10.1142/S0219749916500349

    Article  MATH  Google Scholar 

  57. Qiang, W.C., Sun, G.H., Dong, Q., Camacho-Nieto, O., Dong, S.H.: Concurrence of three Jaynes-Cummings systems. Quantum Inf. Process. 17(4), 90 (2018). https://doi.org/10.1007/s11128-018-1851-8

    Article  ADS  MathSciNet  MATH  Google Scholar 

  58. Qiang, W.C., Sun, G.H., Dong, Q., Dong, S.H.: Genuine multipartite concurrence for entanglement of Dirac fields in noninertial frames. Phys. Rev. A (2018). https://doi.org/10.1103/physreva.98.022320

    Article  Google Scholar 

  59. Dong, Q., Manilla, A.A.S., Yáñez, I.L., Sun, G.H., Dong, S.H.: Tetrapartite entanglement measures of GHZ state with uniform acceleration. Phys. Scr. 94(10), 105101 (2019). https://doi.org/10.1088/1402-4896/ab2111

    Article  ADS  Google Scholar 

  60. Dong, Q., Sanchez, M.A.M., Sun, G.H., Toutounji, M., Dong, S.H.: Tripartite entanglement measures of generalized GHZ state in uniform acceleration. Chin. Phys. Lett. 36(10), 100301 (2019). https://doi.org/10.1088/0256-307x/36/10/100301

    Article  ADS  Google Scholar 

  61. Amir, A., Lahini, Y., Perets, H.B.: Classical diffusion of a quantum particle in a noisy environment. Phys. Rev. E (2009). https://doi.org/10.1103/physreve.79.050105

    Article  Google Scholar 

  62. Thompson, C., Vemuri, G., Agarwal, G.S.: Anderson localization with second quantized fields in a coupled array of waveguides. Phys. Rev. A (2010). https://doi.org/10.1103/physreva.82.053805

    Article  Google Scholar 

  63. Lahini, Y., Bromberg, Y., Christodoulides, D.N., Silberberg, Y.: Quantum correlations in two-particle anderson localization. Phys. Rev. Lett. (2010). https://doi.org/10.1103/physrevlett.105.163905

    Article  Google Scholar 

  64. Oppenheim, A.V., Verghese, G.C.: Signals, Systems and Inference. Pearson, London (2015)

    Google Scholar 

  65. Bordone, P., Buscemi, F., Benedetti, C.: Effect of Markov and Non-markov classical noise on entanglement dynamics. Fluctuation Noise Lett. 11(03), 1242003 (2012). https://doi.org/10.1142/s0219477512420035

    Article  Google Scholar 

  66. Faoro, L., Ioffe, L.B.: Microscopic origin of low-frequency flux noise in Josephson circuits. Phys. Rev. Lett. (2008). https://doi.org/10.1103/physrevlett.100.227005

    Article  Google Scholar 

  67. Bergli, J., Galperin, Y.M., Altshuler, B.L.: Decoherence in qubits due to low-frequency noise. New J. Phys. 11(2), 025002 (2009). https://doi.org/10.1088/1367-2630/11/2/025002

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kuate Fodouop Fabrice.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fabrice, K.F., Arthur, T.T., Pernel, N.N. et al. Tripartite quantum discord dynamics in qubits driven by the joint influence of distinct classical noises. Quantum Inf Process 20, 20 (2021). https://doi.org/10.1007/s11128-020-02967-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02967-0

Keywords

Navigation