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Dynamical behavior of quantum correlations between two qubits coupled to an external environment

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Abstract

We investigate the dynamics of quantum correlations of a two-qubit system coupled to an external environment. We have considered both cases: a spin environment and a bosonic environment. In all cases, we have chosen the Bell-diagonal state as the initial state and computed the evolution of quantum correlations in terms of entanglement, quantum discord and trace distance geometric quantum discord. Special attention is paid to the singular quantum phenomena, such as entanglement sudden death, sudden transition and double sudden transitions from classical to quantum decoherence, which all depend on the initial state and the parameters related to the system and the environment. We find the trace distance geometric quantum discord has a good robustness in resisting the spin and bosonic environmental noise.

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References

  1. Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)

    Article  ADS  Google Scholar 

  2. Ladd, T.D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J.L.: Quantum computers. Nature 464, 45 (2010)

    Article  ADS  Google Scholar 

  3. Aolita, L., deMelo, F., Davidovich, L.: Open-system dynamics of entanglement:a key issues review. Rep. Prog. Phys. 78, 042001 (2015)

    Article  ADS  Google Scholar 

  4. Orieux, A., D’Arrigo, A., Ferranti, A., Franco, G., 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. 5, 8575 (2015)

    Article  ADS  Google Scholar 

  5. Man, Z.X., Xia, Y.J., Franco, RLo: Cavity-based architecture to preserve quantum coherence and entanglement. Sci. Rep. 5, 13843 (2015)

    Article  ADS  Google Scholar 

  6. Franco, R.L.: Switching quantum memory on and off. New J. Phys 17, 081004 (2015)

    Article  Google Scholar 

  7. Salles, A., de Melo, F., Almeida, M.P., Hor-Meyll, M., Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L.: Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment. Phys. Rev. A 78, 022322 (2008)

    Article  ADS  Google Scholar 

  8. Franco, R.L., D’Arrigo, A., Falci, G., Compagno, G., Paladino, E.: Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling. Phys. Rev. B 90, 054304 (2014)

    Article  ADS  Google Scholar 

  9. D’Arrigo, A., Franco, R.L., Benenti, G., Paladino, E., Falci, G.: Recovering entanglement by loccal operations. Ann. Phys. 350, 211 (2014)

    Article  ADS  Google Scholar 

  10. D’Arrigo, A., Benenti, G., Franco, RLo, Falci, G., Paladino, E.: Hidden entanglement, system-environment information flow and non-Markovianity. Int. J. Quantum Inf. 12, 1461005 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yu, T., Eberly, J.H.: Finite-Time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)

    Article  ADS  Google Scholar 

  12. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  MATH  Google Scholar 

  13. Ali, M., Rau, A.R.P., Alber, G.: Erratum: quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)

    Article  ADS  Google Scholar 

  14. Dakic, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  MATH  Google Scholar 

  15. Luo, S.L., Fu, S.S.: Geometric measure of quantum discord. Phys. Rev. A 82, 034302 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Zhou, T., Cui, J.X., Long, G.L.: Measure of nonclassical correlation in coherence-vector representation. Phys. Rev. A 84, 062105 (2011)

    Article  ADS  Google Scholar 

  17. Hassan, A.S.M., Lari, B., Joag, P.S.: Tight lower bound to the geometric measure of quantum discord. Phys. Rev. A 85, 024302 (2012)

    Article  ADS  Google Scholar 

  18. Xu, J.S., Sun, K., Li, C.F., Xu, X.Y., Guo, G.C.: Experimental recovery of quantum correlations in absence of system-enviroment back-action. Nat. Commun. 4, 2851 (2013)

    ADS  Google Scholar 

  19. 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 92, 032311 (2015)

    Article  ADS  Google Scholar 

  20. Bellomo, B., Compagno, G., Franco, R.L., Ridolfo, A., Savasta, S.: dynamics and extraction ofquantum discord in a multipartite open system. Int. J. Quantum Inf. 9, 1665 (2011)

    Article  MATH  Google Scholar 

  21. Bellomo, B., Franco, R.L., Compagno, G.: Dynamics of geometric and entropic quantifiers of correlations in open quantum systems. Phys. Rev. A 86, 012312 (2012)

    Article  ADS  Google Scholar 

  22. Lanyon, B.P., Barbieri, M., Almedia, M.P., White, A.G.: Experimental quantum computing without entanglement. Phys. Rev. Lett. 101, 200501 (2008)

    Article  ADS  Google Scholar 

  23. Modi, K., Brodutch, A., Cable, H., Paterek, T., Vedral, V.: The classical-quantum boundary for correlations: discord and related measures. Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  24. Mazzola, L., Piilo, J., Maniscalco, S.: Sudden transition between classical and quantum decoherence. Phys. Rev. Lett. 104, 200401 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  25. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  26. Guo, J.L., Mi, Y.J., Song, H.S.: Quantum discord dynamics of two-qubit system in a quantum spin environment. Eur. Phys. J. D 66, 24 (2012)

    Article  ADS  Google Scholar 

  27. Guo, J.L., Mi, Y.J., Zhang, J., Song, H.S.: Thermal quantum discord of spins in an inhomogeneous magnetic field. J. Phys. B At. Mol. Opt. Phys. 44, 065504 (2011)

    Article  ADS  Google Scholar 

  28. Sarandy, M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A 80, 022108 (2009)

    Article  ADS  Google Scholar 

  29. Mi, Y.J.: Classical correlation and quantum discord in a two qubit system under dissipation environments. Int. J. Theor. Phys. 51, 544 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  30. He, Q.L., Xu, J.B., Yao, D.X., Zhang, Y.Q.: Sudden transition between classical and quantum decoherence in dissipative cavity QED and stationary quantum discord. Phys. Rev. A 84, 022312 (2011)

    Article  ADS  Google Scholar 

  31. Luo, D.W., Lin, H.Q., Xu, J.B., Yao, D.X.: Pulse control of sudden transition for two qubits in XY spin baths and quantum phase transition. Phys. Rev. A 84, 062112 (2011)

    Article  ADS  Google Scholar 

  32. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  33. Bellomo, B., Giorgi, G.L., Galve, F., Franco, RLo, Compagno, G., Zambrini, R.: Unified view of correlations using the square-norm distance. Phys. Rev. A 85, 032104 (2012)

    Article  ADS  Google Scholar 

  34. Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)

    Article  ADS  Google Scholar 

  35. Nakano, T., Piani, M., Adesso, G.: Negativity of quantumness and its interpretations. Phys. Rev. A 88, 012117 (2013)

    Article  ADS  Google Scholar 

  36. Spehner, D., Orszag, M.: Geometric quantum discord with Bures distance. New J. Phys. 15, 103001 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  37. Bromley, T.R., Cianciaruso, M., Franco, RLo, Adesso, G.: Unifying approach to the quantification of bipartite correlations by Bures distance. J. Phys. A 47, 405302 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  38. Hu, X., Fan, H., Zhou, D.L., Liu, W.M.: Quantum correlating power of local quantum channels. Phys. Rev. A 87, 032340 (2013)

    Article  ADS  Google Scholar 

  39. Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012)

    Article  ADS  Google Scholar 

  40. Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038 (2014)

    Article  ADS  Google Scholar 

  41. Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115 (2013)

    Article  ADS  Google Scholar 

  42. Paula, F.M., Silva, I.A., Montealegre, J.D., Souza, A.M., deAzevedo, E.R., Sarthour, R.S., Saguia, A., Oliveira, I.S., Soares-Pinto, D.O., Adesso, G., Sarandy, M.S.: Observation of environment-induced double sudden transitions in geometric quantum correlations. Phys. Rev. Lett. 111, 250401 (2013)

    Article  ADS  Google Scholar 

  43. Luo, D.W., Xu, J.B.: Sudden transitions and scaling behavior of geometric quantum correlation for two qubits in quantum critical environments at finite temperature. J. Phys. A 47, 365302 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  44. Aaronson, B., Franco, RLo, Adesso, G.: Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence. Phys. Rev. A 88, 012120 (2013)

    Article  ADS  Google Scholar 

  45. Aaronson, B., Franco, RLo, Compagno, G., Adesso, G.: Hierarchy and dynamics of trace distance correlations. New J. Phys. 15, 093022 (2014)

    Article  Google Scholar 

  46. Cianciaruso, M., Bromley, T.R., Roga, W., Franco, RLo, Adesso, G.: Universal freezing of quantum correlations within the geometric approach. Sci. Rep. 5, 10177 (2015)

    Article  ADS  Google Scholar 

  47. Silva, I.A., Souza, A.M., Bromley, T.R., Cianciaruso, M., Sarthour, R.S., Oliveira, I.S., Franco, R.Lo., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Observation of time-invariant coherence in a room temperature quantum simulator. arXiv:1511.01971 (2015)

  48. Lombardo, F.C., Villar, P.I.: Environmentally induced effects on a bipartite two-level system: geometric phase and entanglement properties. Phys. Rev. A 81, 022115 (2010)

    Article  ADS  Google Scholar 

  49. Franco, RLo, Bellomo, B., Maniscalco, S., Compagno, G.: dynamics of correlations in two-qubit systems within non-Markovian environments. Int. J. Mod. Phys. B 27, 1345053 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  51. Obando, P.C., Paula, F.M., Sarandy, M.S.: Trace-distance correlations for X states and the emergence of the pointer basis in Markovian and non-Markovian regimes. Phys. Rev. A 92, 032307 (2015)

    Article  ADS  Google Scholar 

  52. Piani, M., Gharibian, S., Adesso, G., Calsamiglia, J.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)

    Article  ADS  Google Scholar 

  53. Silva, I.A., Girolami, D., Auccaise, R., Sarthour, R.S., Oliveira, I.S., Bonagamba, T.J., deAzevedo, E.R., Soares-Pinto, D.O., Adesso, G.: Measuring bipartite quantum correlations of an unknown state. Phys. Rev. Lett. 110, 140501 (2013)

    Article  ADS  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China Grant Nos. 11305114, 11304226 and 11505126.

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Authors and Affiliations

  1. College of Physics and Materials Science, Tianjin Normal University, Tianjin, 300387, China

    Jin-Long Wei, Xing-Li Li, Xi-Zheng Zhang & Jin-Liang Guo

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  1. Jin-Long Wei
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Correspondence to Jin-Liang Guo.

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Wei, JL., Li, XL., Zhang, XZ. et al. Dynamical behavior of quantum correlations between two qubits coupled to an external environment. Quantum Inf Process 15, 2425–2440 (2016). https://doi.org/10.1007/s11128-016-1277-0

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