Skip to main content

Advertisement

Springer Nature Link
Log in

Robust correlations in a dissipative two-qubit system interacting with two coupled fields in a non-degenerate parametric amplifier

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The collective model of two qubit systems with an intrinsic decoherence effect is analytically explored. Each qubit system interacts with two coupled fields in the non-degenerate parametric amplifier (via two-photon non-degenerate transitions). We investigate the dynamics of the Bures entanglement and non-local correlations based on the trace-norm measurement-induced non-locality and the maximum Bell function. Under different considerations (initial coherence intensities of the two coupled fields, resonance detunings, and intrinsic decoherence), the robustness of the initial quantum correlations is investigated. We show that the sudden death and birth of Bures entanglement, the stationary correlation of trace-norm as well as the Bell-function correlations can be controlled. The trace-norm measurement-induced non-locality presents a good robustness against the intrinsic decoherence and the detuning, unlike the maximal Bell-function correlation and Bures entanglement.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Majer, J., Chow, J.M., Gambetta, J.M., Koch, J., Johnson, B.R., Schreier, J.A., Frunzio, L., Schuster, D.I., Houck, A.A., Wallraff, A., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Coupling superconducting qubits via a cavity bus. Nature 449, 443 (2007)

    Article  ADS  Google Scholar 

  2. Duan, L.M., Lukin, M.D., Cirac, J.I., Zoller, P.: Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413 (2001)

    Article  ADS  Google Scholar 

  3. Roch, N., Schwartz, M.E., Motzoi, F., Macklin, C., Vijay, R., Eddins, A.W., Korotkov, A.N., Whaley, K.B., Sarovar, M., Siddiqi, I.: Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits. Phys. Rev. Lett. 112, 170501 (2014)

    Article  ADS  Google Scholar 

  4. Obada, A.-S.F., Hessian, H.A., Mohamed, A.-B.A., Homid, A.H.: Efficient protocol of N-bit discrete quantum Fourier transform via transmon qubits coupled to a resonator. Quantum Inf. Process. 13, 475 (2014)

    Article  ADS  Google Scholar 

  5. Obada, A.-S.F., Hessian, H.A., Mohamed, A.-B.A., Homid, A.H.: Implementing discrete quantum Fourier transform via superconducting qubits coupled to a superconducting cavity. J. Opt. Soc. Am. B 30, 1178 (2013)

    Article  ADS  Google Scholar 

  6. Lin, J.-B., Liang, Y., Song, C., Ji, X., Zhang, S.: Generation of 3D entanglement between two spatially separated atoms via shortcuts to adiabatic passage. J. Opt. Soc. Am. B 33, 519 (2016)

    Article  ADS  Google Scholar 

  7. Mohamed, A.-B.A., Hessian, H.A.: Non-classical correlations in the general state of two SC-qubit with a phase damping: non-local correlation and geometric discord. J. Mod. Opt. 64, 521 (2017)

    Article  ADS  Google Scholar 

  8. Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Majer, J., Devoret, M., Girvin, S.M., Schoelkopf, R.J.: Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005)

    Article  ADS  Google Scholar 

  9. Mohamed, A.-B.A., Eleuch, H.: Non-classical effects in cavity QED containing a nonlinear optical medium and a quantum well Entanglement and non-Gaussanity. Eur. Phys. J. D 69, 191 (2015)

    Article  ADS  Google Scholar 

  10. Mohamed, A.-B.A.: Quantum correlation of correlated two qubits interacting with a thermal field. Phys. Scr. 85, 055013 (2012)

    Article  ADS  Google Scholar 

  11. Mohamed, A.-B.A., Joshi, A., Hassan, S.S.: Bipartite non-local correlations in a double-quantum-dot excitonic system. J. Phys. A 33, 335301 (2014)

    Article  MathSciNet  Google Scholar 

  12. Sete, E.A., Eleuch, H., Ooi, C.H.R.: Entanglement between exciton and mechanical modes via dissipation-induced coupling. Phys. Rev. A 92, 033843 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. 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 

  15. Obada, A.-S.F., Hessian, H.A., Mohamed, A.-B.A.: Influence of phase damping on the entanglement for the damped JC model in the pure and mixed states. Laser Phys. 18, 1111 (2008)

    Article  ADS  Google Scholar 

  16. Mohamed, A.-B.A.: Long-time death of nonclassicality of a cavity field interacting with a charge qubit and its own reservoir. Phys. Lett. A 374, 4115 (2010)

    Article  ADS  Google Scholar 

  17. Mohamed, A.-B.A., Eleuch, H.: Generation and robustness of bipartite non-classical correlations in two nonlinear microcavities coupled by an optical fiber. J. Opt. Soc. Am. B 35, 47 (2018)

    Article  ADS  Google Scholar 

  18. Sete, E.A., Eleuch, H.: Strong squeezing and robust entanglement in cavity electromechanics. Phys. Rev. A 89, 013841 (2014)

    Article  ADS  Google Scholar 

  19. Eleuch, H., Rotter, I.: Open quantum systems and Dicke superradiance. Eur. Phys. J. D 68, 74 (2014)

    Article  ADS  Google Scholar 

  20. Clauser, J.F., Horne, M.A., Shimony, A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969)

    Article  ADS  Google Scholar 

  21. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Luo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Hu, M.L., Fan, H.: Measurement-induced nonlocality based on the trace norm. New J. Phys. 17, 033004 (2015)

    Article  ADS  Google Scholar 

  27. Hu, M.-L., Hu, X., Wang, J., Peng, Y., Zhang, Y.-R., Fan, H.: Quantum coherence and geometric quantum discord. Phys. Rep. 762, 1–100 (2018)

    ADS  MathSciNet  MATH  Google Scholar 

  28. 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 

  29. Mohamed, A.-B.A.: Bipartite non-classical correlations for a lossy two connected qubit-cavity systems: trace distance discord and Bell’s non-locality. Quantum Inf. Process. 17, 96 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  30. Mohamed, A.-B.A., Metwally, N.: Enhancing non-local correlations in a dissipative two-qubit system via dipole dipole interplay. Quantum Inf. Process. 18, 79 (2019)

    Article  ADS  Google Scholar 

  31. Xi, Z., Wang, X., Li, Y.: Measurement-induced nonlocality based on the relative entropy. Phys. Rev. A 85, 042325 (2012)

    Article  ADS  Google Scholar 

  32. Wigner, E.P., Yanase, M.M.: Information contents of distributions. Proc. Natl. Acad. Sci. USA 49, 910 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  33. Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)

    Article  ADS  Google Scholar 

  34. Wu, S.-X., Zhang, J., Yu, C.-S., Song, H.-S.: Uncertainty-induced quantum nonlocality. Phys. Lett. A 378, 344 (2014)

    Article  ADS  Google Scholar 

  35. Mohamed, A.-B.A., Eleuch, H.: Quantum correlation control for two semiconductor microcavities connected by an optical fiber. Phys. Scr. 92, 065101 (2017)

    Article  ADS  Google Scholar 

  36. Mohamed, A.-B.A., Eleuch, H.: Stationary quantum correlation and coherence of two-mode Kerr nonlinear coupler interdicting with Su(2)-system under intrinsic damping. J. Mod. Opt. 65, 2213 (2018)

    ADS  Google Scholar 

  37. DiVincenzo, D.P.: The physical implementation of quantum computation. Fortschr. Phys. 48, 771 (2000)

    Article  Google Scholar 

  38. Milburn, G.J.: Intrinsic decoherence in quantum mechanics. Phys. Rev. A 44, 5401 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  39. Mohamed, A.-B.A.: Non-local correlations via Wigner-Yanase skew information in two SC-qubit having mutual interaction under phase decoherence. Eur. Phys. J. D 71, 261 (2017)

    Article  ADS  Google Scholar 

  40. Coulamy, I.B., Warnes, J.H., Sarandy, M.S., Saguia, A.: Scaling of the local quantum uncertainty at quantum phase transitions. Phys. Lett. A 380, 1724 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  41. Wu, Y.-L., Deng, D.-L., Li, X., Sarma, S.D.: Intrinsic decoherence in isolated quantum systems. Phys. Rev. B 95, 014202 (2017)

    Article  ADS  Google Scholar 

  42. Mohamed, A.-B.A., Metwally, N.: Non-classical correlations based on skew information for an entangled two qubit-system with non-mutual interaction under intrinsic decoherence. Ann. Phys. 381, 137 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  43. Khalil, E.M., Abdalla, M.S., Obada, A.S.-F.: Pair entanglement of two-level atoms in the presence of a nondegenerate parametric amplifier. J. Phys. B 43, 095507 (2010)

    Article  ADS  Google Scholar 

  44. Bashkirov, E.K.: Dynamics of the two-atom jaynes-cummings model with nondegenerate two-photon transitions. Laser Phys. 16, 1218 (2006)

    Article  ADS  Google Scholar 

  45. Bashkirov, E.K., Mastyugin, M.S.: The influence of the dipole-dipole interaction and atomic coherence on the entanglement of two atoms with degenerate two-photon transitions. Opt. Spectrosc. 116, 630 (2014)

    Article  ADS  Google Scholar 

  46. You, J.Q., Nori, F.: Atomic physics and quantum optics using superconducting circuits. Nature 474, 589 (2011)

    Article  ADS  Google Scholar 

  47. Bashkirov, E.K., Mastyugin, M.S.: The dynamics of entanglement in two-atom Tavis-Cummings model with non-degenerate two-photon transitions for four-qubits initial atom-field entangled states. Opt. Commun. 313, 170 (2014)

    Article  ADS  Google Scholar 

  48. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)

    Article  ADS  Google Scholar 

  49. Obada, A.-S.F., Mohamed, A.-B.A.: Death of entanglement and non-locality in a superconducting qubit-field entangled state in a thermal reservoir. Opt. Commun. 285, 3027 (2012)

    Article  ADS  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. Streltsov, A., Kampermann, H., Bruss, D.: Linking a distance measure of entanglement to its convex roof. New J. Phys. 12, 123004 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  53. Mohamed, A.-B.A., Hessian, H.A., Obada, A.-S.F.: Entanglement sudden death of a SC-qubit strongly coupled with a quantized mode of a lossy cavity. Phys. A 390, 519 (2011)

    Article  Google Scholar 

  54. Obada, A.-S.F., Mohamed, A.-B.A.: Death of entanglement and non-locality in a superconducting qubit-field entangled state in a thermal reservoir. Opt. Commun. 285, 3027 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank the referees for their useful remarks, which helped us to improve the manuscript.

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia

    A.-B. A. Mohamed

  2. Faculty of Science, Assiut University, Assiut, Egypt

    A.-B. A. Mohamed

  3. Faculty of Science, Al-Baha University, Al-Baha, Saudi Arabia

    H. A. Hessian

  4. Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi University, Abu Dhabi, UAE

    H. Eleuch

  5. Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX, 77843, USA

    H. Eleuch

Authors
  1. A.-B. A. Mohamed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. A. Hessian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Eleuch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A.-B. A. Mohamed.

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

Mohamed, AB.A., Hessian, H.A. & Eleuch, H. Robust correlations in a dissipative two-qubit system interacting with two coupled fields in a non-degenerate parametric amplifier. Quantum Inf Process 18, 327 (2019). https://doi.org/10.1007/s11128-019-2443-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2443-y

Keywords