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Quantum Information Processing

, Volume 14, Issue 7, pp 2517–2533 | Cite as

Effect of local filtering on freezing phenomena of quantum correlation

  • Sumana Karmakar
  • Ajoy Sen
  • Amit Bhar
  • Debasis Sarkar
Article

Abstract

General quantum correlation measures such as quantum discord, one-norm geometric quantum discord exhibit freezing, sudden change, and double sudden change behavior in their decay rates under different noisy channels. Therefore, one may attempt to investigate how the freezing behavior and other dynamical features are affected under application of local quantum operations. In this work, we demonstrate the effect of local filtering on the dynamical evolution of quantum correlations. We have found that using local filtering, one may remove freezing depending upon the filtering parameter.

Keywords

Quantum correlation Discord Local filtering Freezing 

Notes

Acknowledgments

The authors S. Karmakar and A. Sen acknowledge the financial support from University Grants Commission, New Delhi, India.

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Datta, A., Shaji, A., Cover, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 100, 050502 (2008)ADSCrossRefGoogle Scholar
  2. 2.
    Olliver, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    Modi, K., Cable, H., Williamson, M., Vedral, V.: Quantum correlations in mixed-state metrology. Phys. Rev. X 1, 021022 (2011)Google Scholar
  4. 4.
    Girolami, D., Tufarelli, T., Adesso, G.: Characterizing Nonclassical Correlations via Local Quantum Uncertainty. Phys. Rev. Lett. 110, 240402 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    Girolami, D., Souza, A.M., Giovannetti, V., Tufarelli, T., Filgueiras, J.G., Sarthour, R.S., Soares-Pinto, D.O., Oliveira, I.S., Adesso, G.: Quantum discord determines the interferometric power of quantum states. Phys. Rev. Lett. 112, 210401 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    Streltsov, A., Kampermann, H., Bruß, D.: Linking quantum discord to entanglement in a measurement. Phys. Rev. Lett. 106, 160401 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    Piani, M., Gharibian, S., Adesso, G., Calsamiglia, J., Horodecki, P., Winter, A.: All nonclassical correlations can be activated into distillable entanglement. Phys. Rev. Lett. 106, 220403 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    Adesso, G., D’Ambrosio, V., Nagali, E., Piani, M., Sciarrino, F.: Experimental entanglement activation from discord in a programmable quantum measurement. Phys. Rev. Lett. 112, 140501 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    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, 671–675 (2012)CrossRefGoogle Scholar
  10. 10.
    Streltsov, A., Zurek, W.H.: Quantum discord cannot be shared. Phys. Rev. Lett. 111, 040401 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    Xiang, G.-Y., Li, J., Yu, B., Guo, G.-C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    Killoran, N., Biggerstaff, D.N., Kaltenback, R., Resch, K.J., Lütkenhaus, N.: Derivation and experimental test of fidelity benchmarks for remote preparation of arbitrary qubit states. Phys. Rev. A 81, 012334 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    Bellomo, B., Compagno, G., Lo Franco, R., Ridolfo, A., Savasta, S.: Dynamics and extraction of quantum discord in a multipartite open system. Int. J. Quantum Inf. 9, 1665 (2011)MATHCrossRefGoogle Scholar
  14. 14.
    Bellomo, B., Lo Franco, R., Compagno, G.: Dynamics of geometric and entropic quantifiers of correlations in open quantum systems. Phys. Rev. A 86, 012312 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    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)ADSCrossRefGoogle Scholar
  16. 16.
    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)MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Xu, J.-S., Sun, K., Li, C.-F., Xu, X.-Y., Guo, G.-C., Andersson, E., Lo Franco, R., Compagno, G.: Experimental recovery of quantum correlations in absence of system-environment back-action. Nat. Commun. 4, 2851 (2013)ADSGoogle Scholar
  18. 18.
    Lo Franco, R., Bellomo, B., Andersson, E., Compagno, G.: Revival of quantum correlations without system-environment back-action. Phys. Rev. A 85, 032318 (2012)ADSCrossRefGoogle Scholar
  19. 19.
    Yu, T., Eberly, J.H.: Sudden death of entanglement. Science 323, 598 (2009)MATHMathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Werlang, T., Souza, S., Fanchini, F.F., Villas Boas, C.J.: Robustness of quantum discord to sudden death. Phys. Rev. A 80, 024103 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    Lang, M.D., Caves, C.M.: Quantum discord and the geometry of Bell-diagonal states. Phys. Rev. Lett. 105, 150501 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    Mazzola, L., Piilo, J., Maniscalco, S.: Sudden transition between classical and quantum decoherence. Phys. Rev. Lett. 104, 200401 (2010)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Aaronson, B., Franco, R.L., Adesso, G.: Comparative investigation of the freezing phenomena for quantum correlations under nondissipative decoherence. Phys. Rev. A 88, 012120 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    Maziero, J., Cěleri, L.C., Serra, R.M., Vedral, V.: Classical and quantum correlations under decoherence. Phys. Rev. A 80, 044102 (2009)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    Cianciaruso, M., Bromley, T. R., Roga, W., Lo Franco R., Adesso, G.: Universal freezing of quantum correlations within the geometric approach. arxiv:1411.2978 (2014)
  26. 26.
    Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)MATHMathSciNetADSCrossRefGoogle Scholar
  27. 27.
    Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Vedral, V., Plenio, M.B.: Entanglement measures and purification procedures. Phys. Rev. A 57, 1619 (1998)ADSCrossRefGoogle Scholar
  29. 29.
    Spehner, D., Orszag, M.: Geometric quantum discord with Bures distance. New J. Phys. 15, 103001 (2013)MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    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)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Luo, S., Zhang, Q.: Informational distance on quantum-state space. Phys. Rev. A 69, 032106 (2004)MathSciNetADSCrossRefGoogle Scholar
  32. 32.
    Dajka, J., Luczka, J., Hänggi, P.: Distance between quantum states in the presence of initial qubit-environment correlations: a comparative study. Phys. Rev. A 84, 032120 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    Eisert, J., Audenaert, K., Plenio, M.B.: Remarks on entanglement measures and non-local state distinguishability. J. Phys. A Math. Gen. 36, 5605 (2003)MATHMathSciNetADSCrossRefGoogle Scholar
  34. 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)ADSCrossRefGoogle Scholar
  35. 35.
    Aaronson, B., Lo Franco, R., Compagno, G., Adesso, G.: Hierarchy and dynamics of trace distance correlations. New J. Phys. 15, 093022 (2013)ADSCrossRefGoogle Scholar
  36. 36.
    Witte, C., Trucks, M.: A new entanglement measure induced by the Hilbert–Schmidt norm. Phys. Lett. A 257, 14–20 (1999)ADSCrossRefGoogle Scholar
  37. 37.
    Ozawa, M.: Entanglement measures and the Hilbert–Schmidt distance. Phys. Lett. A 268, 158–160 (2000)MATHMathSciNetADSCrossRefGoogle Scholar
  38. 38.
    Dakić, B., Vedral, V., Brukner, Č.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    Dakić, B., Lipp, Y.O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, Č., Walther, P.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012)CrossRefGoogle Scholar
  40. 40.
    Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012)ADSCrossRefGoogle Scholar
  41. 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)ADSCrossRefGoogle Scholar
  42. 42.
    Pan, J.-W., Simon, C., Brukner, Č., Zeilinger, A.: Entanglement purification for quantum communication. Nature 410, 1067 (2001)ADSCrossRefGoogle Scholar
  43. 43.
    Yamamoto, T., Koashi, M., Özdemir, S.K., Imoto, N.: Experimental extraction of an entangled photon pair from two 11 identically decohered pairs. Nature 421, 343 (2003)ADSCrossRefGoogle Scholar
  44. 44.
    Siomau, M., Kamli, Ali A.: Defeating entanglement sudden death by a single local filtering. Phys. Rev. A 86, 032304 (2012)ADSCrossRefGoogle Scholar
  45. 45.
    Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A Math. Gen. 34, 6899 (2001)MATHMathSciNetADSCrossRefGoogle Scholar
  46. 46.
    Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)ADSCrossRefGoogle Scholar
  47. 47.
    You, B., Cen, L.-X.: Necessary and sufficient conditions for the freezing phenomena of quantum discord under phase damping. Phys. Rev. A 86, 012102 (2012)ADSCrossRefGoogle Scholar
  48. 48.
    Paula, F.M., Montealegre, J.D., Saguia, A., de Oliveria, Thiago R., Sarandy, M.S.: Geometric classical and total correlations via trace distance. Europhys. Lett. 103, 50008 (2013)ADSCrossRefGoogle Scholar
  49. 49.
    Gisin, N.: Hidden quantum nonlocality revealed by local filters. Phys. Lett. A 210, 151–156 (1996)MATHMathSciNetADSCrossRefGoogle Scholar
  50. 50.
    Hirsch, F., Quintino, M.T., Bowles, J., Brunner, N.: Genuine hidden quantum nonlocality. Phys. Rev. Lett. 111, 160402 (2013)ADSCrossRefGoogle Scholar
  51. 51.
    Sun, Q., Al-Amri, M., Davidovich, L., Suhail Zubairy, M.: Reversing entanglement change by a weak measurement. Phys. Rev. A 82, 052323 (2010)ADSCrossRefGoogle Scholar
  52. 52.
    Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. Rev. A 84, 042313 (2011)ADSCrossRefGoogle Scholar
  53. 53.
    Ciccarellol, F., Tufarelli, T., Giovannetti, V.: Toward computability of trace distance discord. New J. Phys. 16, 013038 (2014)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Sumana Karmakar
    • 1
  • Ajoy Sen
    • 1
  • Amit Bhar
    • 2
  • Debasis Sarkar
    • 1
  1. 1.Department of Applied MathematicsUniversity of CalcuttaKolkataIndia
  2. 2.Department of MathematicsJogesh Chandra Chaudhuri CollegeKolkataIndia

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