Quantum Discord in Nuclear Magnetic Resonance Systems at Room Temperature

Abstract

We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Notes

  1. 1.

    Equation (24) contains the typical density operator describing the state of NMR systems.

  2. 2.

    A modified version of this classicality witness was implemented in the optical context [36].

References

  1. 1.

    A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935)

    ADS  MATH  Article  Google Scholar 

  2. 2.

    E. Schrödinger, Proc. Camb. Philos. Soc. 31, 555 (1935)

    ADS  Article  Google Scholar 

  3. 3.

    J.S. Bell, Physica 1, 195 (1964)

    Google Scholar 

  4. 4.

    J.F. Clauser, A. Shimony, Rep. Prog. Phys. 41, 1882 (1978)

    ADS  Article  Google Scholar 

  5. 5.

    A. Aspect, http://arxiv.org/abs/quant-ph/0402001 (2004)

  6. 6.

    N.D. Mermin, Rev. Mod. Phys. 65, 803 (1993)

    MathSciNet  ADS  Article  Google Scholar 

  7. 7.

    R.F. Werner, Phys. Rev. A 40, 4277 (1989)

    ADS  Article  Google Scholar 

  8. 8.

    S. Popescu, Phys. Rev. Lett. 72, 797 (1994)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  9. 9.

    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)

    Google Scholar 

  10. 10.

    M. Piani, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 100, 090502 (2008)

    ADS  Article  Google Scholar 

  11. 11.

    C.E. Shannon, Bell Syst Tech J 27, 379 (1948)

    MathSciNet  MATH  Google Scholar 

  12. 12.

    B. Schumacher, Phys. Rev. A 51, 2738 (1995)

    MathSciNet  ADS  Article  Google Scholar 

  13. 13.

    B. Groisman, S. Popescu, A. Winter, Phys. Rev. A 72, 032317 (2005)

    MathSciNet  ADS  Article  Google Scholar 

  14. 14.

    B. Schumacher, M.D. Westmoreland, Phys. Rev. A 74, 042305 (2006)

    ADS  Article  Google Scholar 

  15. 15.

    H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)

    ADS  Article  Google Scholar 

  16. 16.

    L.C. Céleri, J. Maziero, R.M. Serra, Int. J. Quant. Inf. 9, 1837 (2011)

    MATH  Article  Google Scholar 

  17. 17.

    K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 84, 1655 (2012)

    ADS  Article  Google Scholar 

  18. 18.

    J.A. Jones, Prog. Nucl. Magn. Reson. Spectrosc. 59, 91 (2011)

    Article  Google Scholar 

  19. 19.

    X.-h. Peng, D. Suter, Front. Phys. China 5, 1 (2010)

    ADS  Article  Google Scholar 

  20. 20.

    S.L. Braunstein, C.M. Caves, R. Jozsa, N. Linden, S. Popescu, R. Schack, Phys. Rev. Lett. 83, 1054 (1999)

    ADS  Article  Google Scholar 

  21. 21.

    G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)

    ADS  Article  Google Scholar 

  22. 22.

    R. Jozsa, N. Linden, Proc. R. Soc. Lond. A 459, 2011 (2003)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  23. 23.

    N. Linden, S. Popescu, Phys. Rev. Lett. 87, 047901 (2001)

    ADS  Article  Google Scholar 

  24. 24.

    A. Datta, A. Shaji, C.M. Caves, Phys. Rev. Lett. 100, 050502 (2008)

    ADS  Article  Google Scholar 

  25. 25.

    V. Vedral, Found. Phys. 40, 1141 (2010)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  26. 26.

    A. Datta, A. Shaji, Int. J. Quant. inf. 9, 1787 (2011)

    MathSciNet  MATH  Article  Google Scholar 

  27. 27.

    B. Eastin, http://arxiv.org/abs/1006.4402 (2010)

  28. 28.

    D.O. Soares-Pinto, R. Auccaise, J. Maziero, A. Gavini-Viana, R.M. Serra, L.C. Céleri, Phil. Trans. R. Soc. A 370, 4821 (2012)

    ADS  Article  Google Scholar 

  29. 29.

    J. Maziero, L.C. Céleri, R.M. Serra, http://arxiv.org/abs/1004.2082 (2010)

  30. 30.

    J. Maziero, L.C. Céleri, R.M. Serra, V. Vedral, Phys. Rev. A 80, 044102 (2009)

    MathSciNet  ADS  Article  Google Scholar 

  31. 31.

    L. Mazzola, J. Piilo, S. Maniscalco, Phys. Rev. Lett. 104, 200401 (2010)

    MathSciNet  ADS  Article  Google Scholar 

  32. 32.

    J. Maziero, R.M. Serra, Int. J. Quant. Inf. 10, 1250028 (2012)

    MathSciNet  Article  Google Scholar 

  33. 33.

    D.O. Soares-Pinto, L.C. Céleri, R. Auccaise, F.F. Fanchini, E.R. deAzevedo, J. Maziero, T.J. Bonagamba, R.M. Serra, Phys. Rev. A 81, 062118 (2010)

    ADS  Article  Google Scholar 

  34. 34.

    R. Auccaise, L.C. Céleri, D.O. Soares-Pinto, E.R. deAzevedo, J. Maziero, A.M. Souza, T.J. Bonagamba, R.S. Sarthour, I.S. Oliveira, R.M. Serra, Phys. Rev. Lett. 107, 140403 (2011)

    ADS  Article  Google Scholar 

  35. 35.

    R. Auccaise, J. Maziero, L.C. Céleri, D.O. Soares-Pinto, E.R. deAzevedo, T.J. Bonagamba, R.S. Sarthour, I.S. Oliveira, R.M. Serra, Phys. Rev. Lett. 107, 070501 (2011)

    ADS  Article  Google Scholar 

  36. 36.

    G.H. Aguilar, O. Jiménez Farías, J. Maziero, R.M. Serra, P.H. Souto Ribeiro, S.P. Walborn, Phys. Rev. Lett. 108, 063601 (2012)

    ADS  Article  Google Scholar 

  37. 37.

    I.S. Oliveira, T.J. Bonagamba, R.S. Sarthour, J.C.C. Freitas, E.R. de Azevedo, NMR Quantum Information Processing (Elsevier, Amsterdan, 2007)

    Google Scholar 

  38. 38.

    H. Kampermann, H.W.S. Veeman, J. Chem. Phys. 122, 214108 (2005)

    ADS  Article  Google Scholar 

  39. 39.

    N. Sinha, T.S. Mahesh, K.V. Ramanathan, A. Kumar, J. Chem. Phys. 114, 4415 (2001)

    ADS  Article  Google Scholar 

  40. 40.

    R.S. Sarthour, E.R. deAzevedo, F.A. Bonk, E.L.G. Vidoto, T.J. Bonagamba, A.P. Guimaraes, J.C.C. Freitas, I.S. Oliveira, Phys. Rev. A 68, 022311 (2003)

    ADS  Article  Google Scholar 

  41. 41.

    F.A. Bonk, R.S. Sarthour, E.R. deAzevedo, J.D. Bulnes, G.L. Mantovani, J.C.C. Freitas, T.J. Bonagamba, A.P. Guimaraes, I.S. Oliveira, Phys. Rev. A 69, 42322 (2004)

    Article  Google Scholar 

  42. 42.

    C.P. Slichter, Principles of Magnetic Resonance (Springer, Berlin, 1992)

    Google Scholar 

  43. 43.

    K. Radley, L.W. Reeves, A.S. Tracey, J. Chem. Phys. 80, 174 (1976)

    Article  Google Scholar 

  44. 44.

    G. Jaccard, S. Wimperis, G. Bodenhausen, J. Chem. Phys. 85, 6282 (1986)

    ADS  Article  Google Scholar 

  45. 45.

    R. Auccaise, J. Teles, R.S. Sarthour, T.J. Bonagamba, I.S. Oliveira, E.R. deAzevedo, J. Magn. Reson. 192, 17 (2008)

    ADS  Article  Google Scholar 

  46. 46.

    E. Knill, I.L. Chuang, R. Laflamme, Phys. Rev. A 57, 3348 (1998)

    MathSciNet  ADS  Article  Google Scholar 

  47. 47.

    D.G. Cory, M.D. Price, T.F. Havel, Physica D 120, 82 (1998)

    ADS  Article  Google Scholar 

  48. 48.

    N. Gershenfeld, I.L. Chuang, Science 275, 350 (1997)

    MathSciNet  MATH  Article  Google Scholar 

  49. 49.

    N. Khaneja, R. Brochett, S.J. Glaser, Phys. Rev. A. 63, 032308 (2001)

    ADS  Article  Google Scholar 

  50. 50.

    N. Khaneja, T. Reiss, C. Kehlet et al., J. Magn. Reson. 172, 296 (2005)

    ADS  Article  Google Scholar 

  51. 51.

    E.M. Fortunato, M.A. Pravia, N. Boulant, G. Teklemariam, T.F. Havel, D.G. Cory, J. Chem. Phys. 116, 7599 (2002)

    ADS  Article  Google Scholar 

  52. 52.

    J. Teles, E.R. deAzevedo, R. Auccaise, R.S. Sarthour, I.S. Oliveira, T.J. Bonagamba, J. Chem. Phys. 126, 154506 (2007)

    ADS  Article  Google Scholar 

  53. 53.

    G.L. Long, H.Y. Yan, Y. Sun, J. Opt. B 3, 376 (2001)

    ADS  Article  Google Scholar 

  54. 54.

    G.M. Leskowitz, L.J. Mueller, Phys. Rev. A 69, 052302 (2004)

    ADS  Article  Google Scholar 

  55. 55.

    M. Cramer, M.B. Plenio, S.T. Flammia, R. Somma, D. Gross, S.D. Bartlett, O. Landon-Cardinal, D. Poulin, Y.-K. Liu, Nat. Commun. 1, 149 (2010)

    Article  Google Scholar 

  56. 56.

    D.O. Soares-Pinto, M.H.Y. Moussa, J. Maziero, E.R. deAzevedo, T.J. Bonagamba, R.M. Serra, L.C. Céleri, Phys. Rev. A 83, 062336 (2011)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support from UFABC, CNPq, CAPES, FAPESP, FAPERJ, and Brazilian National Institute of Science and Technology for Quantum Information (INCT-IQ). The warm hospitality of Instituto de Física de São Carlos—Universidade de São Paulo (IFSC-USP) and Centro Brasileiro de Pesquisas Físicas (CBPF), where the experiments were performed, is also acknowledge.

Author information

Affiliations

Authors

Corresponding author

Correspondence to R. M. Serra.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Maziero, J., Auccaise, R., Céleri, L.C. et al. Quantum Discord in Nuclear Magnetic Resonance Systems at Room Temperature. Braz J Phys 43, 86–104 (2013). https://doi.org/10.1007/s13538-013-0118-1

Download citation

Keywords

  • Quantum information
  • Quantum discord
  • Nonclassical correlations
  • Nuclear magnetic resonance