Advertisement

Invertible condition of quantum Fisher information matrix for a mixed qubit

  • Ping Yue
  • Li Ge
  • Qiang ZhengEmail author
Regular Article

Abstract

Estimating multiparamter simultaneously as precise as possible is an important goal of quantum metrology. As a first step to this end, here we give a condition determining whether two arbitrary parameters can be estimated simultaneously for a qubit in the mixed state. An application of this condition is shown.

Graphical abstract

Keywords

Quantum Optics 

References

  1. 1.
    V. Giovanetti, S. Lloyd, L. Maccone, Science 306, 1330 (2004) ADSCrossRefGoogle Scholar
  2. 2.
    N. Hinkley, J.A. Sherman, N.B. Phillips, M. Schioppo, N.D. Lemke, K. Beloy, M. Pizzocaro, C.W. Oates, A.D. Ludlow, Science 341, 1215 (2013) ADSCrossRefGoogle Scholar
  3. 3.
    J.J. Bollinger, W.M. Itano, D.J. Wineland, D.J. Heinzen, Phys. Rev. A 54, R4649 (1996) ADSCrossRefGoogle Scholar
  4. 4.
    J. Aasi et al., (LIGO Scientific Collaboration), Nat. Photon. 7, 613 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    U.L. Andersen, Nat. Photon. 7, 589 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    J.M. Taylor, P. Cappellaro, L. Childress, L. Jiang, D. Budker, P.R. Hemmer, A. Yacoby, R. Walsworth, M.D. Lukin, Nat. Phys. 4, 810 (2008)CrossRefGoogle Scholar
  7. 7.
    B.M. Escher, R.L. de Matos Filho, L. Davidovich, Nat. Phys. 7, 406 (2011)CrossRefGoogle Scholar
  8. 8.
    R. Demkowicz-Dobrzański, J. Kolodyński, M. Gută, Nat. Commun. 3, 1063 (2012). CrossRefGoogle Scholar
  9. 9.
    F. Hudelist, J. Kong, C. Liu, J. Jing, Z.Y. Ou, W.P. Zhang, Nat. Commun. 5, 3049 (2014)ADSCrossRefGoogle Scholar
  10. 10.
    Y.M. Zhang, X.W. Li, W. Yang, G.R. Jin, Phys. Rev. A 88, 043832 (2013) ADSCrossRefGoogle Scholar
  11. 11.
    Q. Zheng, Y. Yao, Y. Li, Eur. Phys. J. D 68, 170 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    W. Zhong, Z. Sun, J. Ma, X.G. Wang, F. Nori, Phys. Rev. A 87, 022337 (2013) ADSCrossRefGoogle Scholar
  13. 13.
    L. Pezzé, A. Smerzi, Phys. Rev. Lett. 102, 100401 (2009) ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    N. Li, S.L. Luo, Phys. Rev. A 88, 014301 (2013) ADSCrossRefGoogle Scholar
  15. 15.
    X.M. Lu, X.G. Wang, C.P. Sun, Phys. Rev. A 82, 042103 (2010) ADSCrossRefGoogle Scholar
  16. 16.
    J. Ma, X.G. Wang, C.P. Sun, F. Nori, Phys. Rep. 509, 89 (2011)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    X.G. Wang, A. Miranowicz, Y.X. Liu, C.P. Sun, F. Nori, Phys. Rev. A 81, 022106 (2010) ADSCrossRefGoogle Scholar
  18. 18.
    H.P. Yuen, M. Lax, IEEE Trans. Inf. Theory 19, 740 (1973)MathSciNetCrossRefGoogle Scholar
  19. 19.
    C. Helstrom, R. Kennedy, IEEE Trans. Inf. Theory 20, 16 (1974)MathSciNetCrossRefGoogle Scholar
  20. 20.
    M.A. Ballester, Phys. Rev. A 69, 022303 (2004) ADSCrossRefGoogle Scholar
  21. 21.
    M.A. Ballester, Phys. Rev. A 70, 032310 (2004) ADSCrossRefGoogle Scholar
  22. 22.
    M.D. Vidrighin, G. Donati, M.G. Genoni, X.M. Jin, W.S. Kolthammer, M.S. Kim, A. Datta, M. Barbieri, I.A. Walmsley, Nat. Commun. 5, 3532 (2014)ADSCrossRefGoogle Scholar
  23. 23.
    R. Vijay, C. Macklin, D.H. Slichter, S.J. Weber, K.W. Murch, R. Naik, A.N. Korotkov, I. Siddiqi, Nature 490, 77 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982)Google Scholar
  25. 25.
    R.A. Fisher, Proc. Cambridge Philos. Soc. 22, 700 (1925)ADSCrossRefGoogle Scholar
  26. 26.
    M.G.A. Paris, Int. J. Quant. Inf. 7, 125 (2009)CrossRefGoogle Scholar
  27. 27.
    S.L. Braunstein, C.M. Caves, Phys. Rev. Lett. 72, 3439 (1994) ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    S.L. Braunstein, C.M. Caves, G.J. Milburn, Ann. Phys. 247, 135 (1996) ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)Google Scholar
  30. 30.
    M.G. Genoni, P. Giorda, M.G.A. Paris, Phys. Rev. A 78, 032303 (2008) ADSCrossRefGoogle Scholar
  31. 31.
    K.C. Young, M. Sarovar, R. Kosut, K.B. Whaley, Phys. Rev. A 79, 062301 (2009) ADSCrossRefGoogle Scholar
  32. 32.
    A. Monras, F. Illuminati, Phys. Rev. A 83, 012315 (2011) ADSCrossRefGoogle Scholar
  33. 33.
    M.G. Genoni, M.G.A. Paris, G. Adesso, H. Nha, P.L. Knight, M.S. Kim, Phys. Rev. A 87, 012107 (2013) ADSCrossRefGoogle Scholar
  34. 34.
    A. Fujiwara, Phys. Rev. A 65, 012316 (2001) ADSCrossRefGoogle Scholar
  35. 35.
    K. Matsumoto, J. Phys. A 35, 3111 (2002) ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    M. Guţǎ, A. Jenčová, Commun. Math. Phys. 276, 341 (2007) ADSCrossRefGoogle Scholar
  37. 37.
    J. Kahn, M. Guţǎ, Commun. Math. Phys. 289, 597 (2009) ADSCrossRefGoogle Scholar
  38. 38.
    P.C. Humphreys, M. Barbieri, A. Datta, I.A. Walmsley, Phys. Rev. Lett. 111, 070403 (2013) ADSCrossRefGoogle Scholar
  39. 39.
    J.D. Yue, Y.R. Zhang, H. Fan, Sci. Rep. 4, 5933 (2014)ADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematics and Computer Science, Guizhou Normal UniversityGuiyangP.R. China
  2. 2.School of Biology and Engineering, Guizhou Medical UniversityGuiyangP.R. China
  3. 3.Division of Quantum Physics and Quantum InformationBeijingP.R. China

Personalised recommendations