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Quantum Information Processing

, Volume 15, Issue 7, pp 2771–2784 | Cite as

The creation of quantum correlation and entropic uncertainty relation in photonic crystals

  • Xue-Min Bai
  • Ning Wang
  • Jun-Qi LiEmail author
  • J.-Q. Liang
Article

Abstract

We investigate the dynamic creation of quantum correlation and entropic uncertainty relation (EUR) in a system of two non-interacting qubits, which are initially prepared in a classically correlated state and subject to the independent radiation in an isotropic or anisotropic photonic bandgap (PBG) crystal environment. It is shown that the detuning condition and environmental structure play a crucial role in controlling the emergence of geometric quantum discord (GQD) and one-norm GQD. In addition, the remarkable similarities and differences for quantum correlation in two PBG environments are also analyzed in detail. Finally, we explore the time evolution of EUR in our model under the influence of PBG environment and present some interesting results.

Keywords

Quantum correlation Environment Entropic uncertainty relation 

Notes

Acknowledgments

This work was supported by the Natural Science Foundation of China under Grants Nos. 11105087, 61275210, 11275118, 11404198 and Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (STIP) under Grant No. 2014102.

References

  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  2. 2.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Vidal, G., Latorre, J.I., Rico, E., Kitaev, A.: Entanglement in quantum critical phenomena. Phys. Rev. Lett. 90, 227902 (2003)ADSCrossRefGoogle Scholar
  4. 4.
    Knill, E., Laflamme, R.: Power of one bit of quantum information. Phys. Rev. Lett. 81, 5672 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    Datta, A., Flammia, S.T., Caves, C.M.: Entanglement and the power of one qubit. Phys. Rev. A 72, 042316 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Datta, A.: Quantum discord between relatively accelerated observers. Phys. Rev. A 80, 052304 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Li, J.-Q., Liang, J.-Q.: Quantum and classical correlations in a classical dephasing environment. Phys. Lett. A 375, 1496 (2011)ADSCrossRefzbMATHGoogle Scholar
  9. 9.
    Madhok, V., Datta, A.: Interpreting quantum discord through quantum state merging. Phys. Rev. A 83, 032323 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    Dakić, B., et al.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012)CrossRefGoogle Scholar
  11. 11.
    Streltsov, A., Kampermann, H., Bruß, D.: Quantum cost for sending entanglement. Phys. Rev. Lett. 108, 250501 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110, 240402 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    Dakić, B., Vedral, V., Brukner, Č.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    Spehner, D., Orszag, M.: Geometric quantum discord with Bures distance. New J. Phys. 15, 103001 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Paula, F.M., de Oliveira, T.R., Sarandy, M.S.: Geometric quantum discord through the Schatten 1-norm. Phys. Rev. A 87, 064101 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    Giorgia, G.L., Roncaglia, M., Raffa, F.A., Genovese, M.: Quantum correlation dynamics in photosynthetic processes assisted by molecular vibrations. Ann. Phys. 361, 72 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wu, W., Luo, D.-W., Xu, J.-B.: Double sudden transitions of geometric discord at finite-temperature in the framework of stochastic description. J. Appl. Phys. 115, 244906 (2014)ADSCrossRefGoogle Scholar
  19. 19.
    Paula, F.M., et al.: Observation of Environment-Induced double sudden transitions in geometric quantum correlations. Phys. Rev. Lett. 111, 250401 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    Eremeev, V., Ciobanu, N., Orszag, M.: Thermal effects on sudden changes and freezing of correlations between remote atoms in a cavity quantum electrodynamics network. Opt. Lett. 39, 2668 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    Benedetti, C., Buscemi, F., Bordone, P., Paris, M.G.A.: Dynamics of quantum correlations in colored-noise environments. Phys. Rev. A 87, 052328 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    Karmakar, S., Sen, A., Bhar, A., Sarkar, D.: Effect of local filtering on freezing phenomena of quantum correlation. Quantum Inf. Process 14, 2517 (2015)ADSCrossRefzbMATHGoogle Scholar
  23. 23.
    Wang, J.C., Jing, J.L., Fan, H.: Quantum discord and measurement-induced disturbance in the background of dilaton black holes. Phys. Rev. D 90, 025032 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    Qiang, W.-C., Zhang, L.: Geometric measure of quantum discord for entanglement of Dirac fields in noninertial frames. Phys. Lett. B 742, 383 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    Yang, W.-L., An, J.-H., Zhang, C.-J., Chen, C.-Y., Oh, C.H.: Dynamics of quantum correlation between separated nitrogen-vacancy centers embedded in plasmonic waveguide. Sci. Rep. 5, 15513 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    Mazzola, L., Piilo, J., Maniscalco, S.: Sudden transition between classical and quantum decoherence. Phys. Rev. Lett. 104, 200401 (2010)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Cianciaruso, M., Bromley, T.R., Roga, W., Franco, R.L., Adesso, G.: Universal freezing of quantum correlations within the geometric approach. Sci. Rep. 5, 10177 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    Chanda, T., Pal, A.K., Biswas, A., Sen(De), A., Sen, U.: Freezing of quantum correlations under local decoherence. Phys. Rev. A 91, 062119 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    Xu, J.-S., et al.: Experimental investigation of classical and quantum correlations under decoherence. Nat. Commun. 1, 7 (2010)ADSGoogle Scholar
  30. 30.
    Auccaise, R., et al.: Environment-Induced sudden transition in quantum discord dynamics. Phys. Rev. Lett. 107, 140403 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    Rong, X., et al.: Experimental protection and revival of quantum correlation in open solid systems. Phys. Rev. B 88, 054419 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    Streltsov, A., Kampermann, H., Bruß, D.: Behavior of quantum correlations under local noise. Phys. Rev. Lett. 107, 170502 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    Hu, X., Gu, Y., Gong, Q., Guo, G.: Necessary and sufficient condition for Markovian-dissipative-dynamics-induced quantum discord. Phys. Rev. A 84, 022113 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    Hu, X., Fan, H., Zhou, D.L., Liu, W.-M.: Necessary and sufficient conditions for local creation of quantum correlation. Phys. Rev. A 85, 032102 (2012)ADSCrossRefGoogle Scholar
  35. 35.
    Guo, Y., Hou, J.: Necessary and sufficient conditions for local creation of quantum discord. J. Phys. A Math. Theor. 46, 155301 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Ciccarello, F., Giovannetti, V.: Creating quantum correlations through local nonunitary memoryless channels. Phys. Rev. A 85, 010102(R) (2012)ADSCrossRefGoogle Scholar
  37. 37.
    Gessner, M., Laine, E.-M., Breuer, H.-P., Piilo, J.: Correlations in quantum states and the local creation of quantum discord. Phys. Rev. A 85, 052122 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    Campbell, S., et al.: Propagation of nonclassical correlations across a quantum spin chain. Phys. Rev. A 84, 052316 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    Gwóźdź, M., Jakóbczyk, L.: Spontaneous emission can locally create quantum discord out of classical correlations. Quantum Inf. Process. 13, 171 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Lanyon, B.P., Jurcevic, P., Hempel, C., Gessner, M., Vedral, V., Blatt, R., Roos, C.F.: Experimental generation of quantum discord via noisy processes. Phys. Rev. Lett. 111, 100504 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    Auccaise, R., et al.: Experimentally witnessing the quantumness of correlations. Phys. Rev. Lett. 107, 070501 (2011)ADSCrossRefGoogle Scholar
  42. 42.
    Orieux, A., Ciampini, M.A., Mataloni, P., Bruß, D., Rossi, M., Macchiavello, C.: Experimental generation of robust entanglement from classical correlations via local dissipation. Phys. Rev. Lett. 115, 160503 (2015)ADSCrossRefGoogle Scholar
  43. 43.
    Prevedel, R., Hamel, D.R., Colbeck, R., Fisher, K., Resch, K.J.: Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement. Nat. Phys. 7, 757 (2011)CrossRefGoogle Scholar
  44. 44.
    Li, C.-F., Xu, J.-S., Xu, X.-Y., Li, K., Guo, G.-C.: Experimental investigation of the entanglement assisted entropic uncertainty principle. Nat. Phys. 7, 752 (2011)CrossRefGoogle Scholar
  45. 45.
    Tomamichel, M., Renner, R.: Uncertainty relation for smooth entropies. Phys. Rev. Lett. 106, 110506 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    Tomamichel, M., Lim, C.C.W., Gisin, N., Renner, R.: Tight finite-key analysis for quantum cryptography. Nat. Commun. 3, 634 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631 (1983)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103 (1988)ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927)ADSCrossRefGoogle Scholar
  50. 50.
    Karpat, G., Piilo, J., Maniscalco, S.: Controlling entropic uncertainty bound through memory effects. Europhys. Lett. 111, 50006 (2015)ADSCrossRefGoogle Scholar
  51. 51.
    Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659 (2010)CrossRefGoogle Scholar
  52. 52.
    Yablonovitch, E., Gmitter, T.J., Leung, K.M.: Photonic band structure: the face-centered-cubic case employing nonspherical atoms. Phys. Rev. Lett. 67, 2295 (1991)ADSCrossRefGoogle Scholar
  53. 53.
    John, S.: Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486 (1987)ADSCrossRefGoogle Scholar
  54. 54.
    Lewenstein, M., Zakrzewski, J., Mossberg, T.W.: Spontaneous emission of atoms coupled to frequency-dependent reservoirs. Phys. Rev. A 38, 808 (1988)ADSCrossRefGoogle Scholar
  55. 55.
    Wu, Y., Wang, J., Mo, M., Zhang, H.Z.: Entanglement manipulation by atomic position in photonic crystals. Opt. Commun. 356, 74 (2015)ADSCrossRefGoogle Scholar
  56. 56.
    Berrada, K.: Protecting the precision of estimation in a photonic crystal. J. Opt. Soc. Am. B 32, 571 (2015)ADSCrossRefGoogle Scholar
  57. 57.
    Huang, J.-H., Chen, Z.-Y., Yu, T.-B., Deng, X.-H., Liu, J.-T., Liu, N.-H.: Dynamics of three-qubit entanglement in photonic crystals. Phys. Rev. A 85, 014301 (2012)ADSCrossRefGoogle Scholar
  58. 58.
    Bellomo, B., LoFranco, R., Compagno, G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99, 160502 (2007)ADSCrossRefGoogle Scholar
  59. 59.
    Montealegre, J.D., Paula, F.M., Saguia, A., Sarandy, M.S.: One-norm geometric quantum discord under decoherence. Phys. Rev. A 87, 042115 (2013)ADSCrossRefGoogle Scholar
  60. 60.
    Ciccarello, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038 (2014)ADSCrossRefGoogle Scholar
  61. 61.
    Li, J.-Q., Cui, X.-L., Liang, J.-Q.: The dynamics of quantum correlation with two controlled qubits under classical dephasing environment. Ann. Phys. 354, 365 (2015)ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    Białynicki-Birula, I., Mycielski, J.: Uncertainty relations for information entropy in wave mechanics. Comm. Math. Phys. 44, 129 (1975)ADSMathSciNetCrossRefGoogle Scholar
  63. 63.
    Kraus, K.: Complementary observables and uncertainty relations. Phys. Rev. D 35, 3070 (1987)ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    Renes, J.M., Boileau, J.-C.: Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009)ADSCrossRefGoogle Scholar
  65. 65.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, p. 931. Academic Press, New York (1980)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Xue-Min Bai
    • 1
  • Ning Wang
    • 1
  • Jun-Qi Li
    • 1
    Email author
  • J.-Q. Liang
    • 1
  1. 1.Institute of Theoretical PhysicsShanxi UniversityTaiyuanChina

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