Quantum Information Processing

, Volume 15, Issue 6, pp 2393–2404

Nonlocality threshold for entanglement under general dephasing evolutions: a case study

Article

Abstract

Determining relationships between different types of quantum correlations in open composite quantum systems is important since it enables the exploitation of a type by knowing the amount of another type. We here review, by giving a formal demonstration, a closed formula of the Bell function, witnessing nonlocality, as a function of the concurrence, quantifying entanglement, valid for a system of two noninteracting qubits initially prepared in extended Werner-like states undergoing any local pure-dephasing evolution. This formula allows for finding nonlocality thresholds for the concurrence depending only on the purity of the initial state. We then utilize these thresholds in a paradigmatic system where the two qubits are locally affected by a quantum environment with an Ohmic class spectrum. We show that steady entanglement can be achieved and provide the lower bound of initial state purity such that this stationary entanglement is above the nonlocality threshold thus guaranteeing the maintenance of nonlocal correlations.

Keywords

Open quantum systems Quantum entanglement Bell nonlocality Pure-dephasing 

References

  1. 1.
    Amico, L., Fazio, R., Osterloh, A., Vedral, V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517576 (2008)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)ADSCrossRefGoogle Scholar
  5. 5.
    Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)MATHGoogle Scholar
  6. 6.
    Rivas, Á., Huelga, S.F., Plenio, M.B.: Quantum non-Markovianity: characterization, quantification and detection. Rep. Prog. Phys. 77, 094001 (2014)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Lo Franco, R., Bellomo, B., Maniscalco, S., Compagno, G.: Dynamics of quantum correlations in two-qubit systems within non-Markovian environments. Int. J. Mod. Phys. B 27, 1345053 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Aolita, L., de Melo, F., Davidovich, L.: Open-system dynamics of entanglement: a key issues review. Rep. Prog. Phys. 78, 042001 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    Ladd, T.D., et al.: Quantum computers. Nature 464, 45 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Schliemann, J., Cirac, J.I., Kus, M., Lewenstein, M., Loss, D.: Quantum correlations in two-fermion systems. Phys. Rev. A 64, 022303 (2001)ADSCrossRefGoogle Scholar
  11. 11.
    Xu, J.-S., et al.: Experimental recovery of quantum correlations in absence of system-environment back-action. Nat. Commun. 4, 2851 (2013)ADSGoogle Scholar
  12. 12.
    D’Arrigo, A., Lo Franco, R., Benenti, G., Paladino, E., Falci, G.: Recovering entanglement by local operations. Ann. Phys. 350, 211 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Orieux, A., et al.: Experimental on-demand recovery of quantum entanglement by local operations within non-Markovian dynamics. Sci. Rep. 5, 8575 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    Mazzola, L., Bellomo, B., Lo Franco, R., Compagno, G.: Connection among entanglement, mixedness and nonlocality in a dynamical context. Phys. Rev. A 81, 052116 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    Horst, B., Bartkiewicz, K., Miranowicz, A.: Two-qubit mixed states more entangled than pure states: comparison of the relative entropy of entanglement for a given nonlocality. Phys. Rev. A 87, 042108 (2013)ADSCrossRefGoogle Scholar
  16. 16.
    Bartkiewicz, K., Horst, B., Lemr, K., Miranowicz, A.: Entanglement estimation from Bell inequality violation. Phys. Rev. A 88, 052105 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)ADSCrossRefGoogle Scholar
  18. 18.
    Gisin, N., Thew, R.: Quantum communication. Nat. Photon 1, 165 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    Lo Franco, R., 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)ADSCrossRefGoogle Scholar
  20. 20.
    Addis, C., Brebner, G., Haikka, P., Maniscalco, S.: Coherence trapping and information backflow in dephasing qubits. J. Phys. Rev. A 89, 024101 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Bellomo, B., Lo Franco, R., Compagno, G.: An optimized Bell test in a dynamical system. Phys. Lett. A 374, 3007 (2010)ADSMathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Horodecki, M., Horodecki, P., Horodecki, R.: Violating Bell inequality by mixed spin-1/2 states: necessary and sufficient condition. Phys. Lett. A 200, 340 (1995)ADSMathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Bellomo, B., Lo Franco, R., Compagno, G.: Entanglement dynamics of two independent qubits in environments with and without memory. J. Phys. Rev. A 77, 032342 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    Bellomo, B., Lo Franco, R., Compagno, G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99, 160502 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    Derkacz, L., Jakóbczyk, L.: Clauser–Horne–Shimony–Holt violation and the entropy-concurrence plane. Phys. Rev. A 72, 042321 (2005)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Gisin, N.: Bell’s inequality holds for all non-product states. Phys. Lett. A 154, 201 (1991)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Verstraete, F., Wolf, M.M.: Entanglement versus Bell violations and their behavior under local filtering operations. Phys. Rev. Lett. 89, 170401 (2002)ADSCrossRefGoogle Scholar
  28. 28.
    Haikka, P., Johnson, T.H., Maniscalco, S.: Non-Markovianity of local dephasing channels and time-invariant discord. Phys. Rev. A 87, 010103(R) (2013)ADSCrossRefGoogle Scholar
  29. 29.
    Bromley, T.R., Cianciaruso, M., Lo Franco, R., Adesso, G.: Unifying approach to the quantification of bipartite correlations by Bures distance. J. Phys. A: Math. Theor. 47, 405302 (2014)MathSciNetCrossRefMATHGoogle Scholar
  30. 30.
    Chiuri, A., Greganti, C., Mazzola, L., Paternostro, M., Mataloni, P.: Linear optics simulation of quantum non-Markovian dynamics. Sci. Rep. 2, 968 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    Pfaff, W., Taminiau, T.H., Robledo, L., Bernien, H., Markham, M., Twitchen, D.J., Hanson, R.: Demonstration of entanglement-by-measurement of solid-state qubits. Nat. Phys. 9, 29 (2013)CrossRefGoogle Scholar
  32. 32.
    Metwally, N.: New aspects of the purity and information of an entangled qubit pair. Int. J. Quantum Inf. 6, 187 (2008)CrossRefGoogle Scholar
  33. 33.
    Tan, J., Kyaw, T.H., Yeo, Y.: Non-Markovian environments and entanglement preservation. Phys. Rev. A 81, 062119 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    Man, Z.-X., Xia, Y.-J., Lo Franco, R.: Cavity-based architecture to preserve quantum coherence and entanglement. Sci. Rep 5, 13843 (2015)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Dipartimento di Energia, Ingegneria dell’Informazione e Modelli MatematiciUniversità di PalermoPalermoItaly

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