Improving Parameters Precision of Quantum Estimation by Homodyne-Based Feedback Control

  • Huangyun RaoEmail author


In this paper, we investigate the improvement of quantum Fisher information (QFI) of a single-qubit system coupled to a common reservoir by homodyne-based feedback control. It is shown that by controlling the polar parameter of the initial quantum state, one may improve the quantum Fisher information of the estimated parameters. By comparing the effects of different feedback control types on QFI, we find that under the homodyne-based feedback control, when the feedback Hamiltonian is selected as λσx, the estimation precision of feedback parameters and dissipation coefficient can be improved.


Parameter estimation Quantum fisher information Homodyne-based feedback control 



This work was supported by Foundation of Science and Technology of Education office of Jiangxi province under Grant No. GJJ170449 and by the National Natural Science Foundation of China under Grant No. 61663016 and 11264015.


  1. 1.
    Giovannetti, V., Lloyd, S., Maccone, L.: Quantum metrology. Phys. Rev. Lett.96(1), 010401 (2006)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bollinger, J.J., Itano, W.M., Wineland, D.J., Heinzen, D.J.: Optimal frequency measurements with maximally correlated states. Phys. Rev. A. 54(6), R4649 (1996)ADSCrossRefGoogle Scholar
  3. 3.
    Huelga, S.F., Macchiavello, C., Pellizzari, T., Ekert, A.K., Plenio, M.B., Cirac, J.I.: Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett.79(20), 3865–3868 (1997)ADSCrossRefGoogle Scholar
  4. 4.
    Taylor, J.M., Cappellaro, P., Childress, L., Jiang, L., Budker, D., Hemmer, P.R., Yacoby, A., Walsworth, R., Lukin, M.D.: High-sensitivity diamond magnetometer with nanoscale resolution. Nat. Phys. 4, 810–816 (2008)CrossRefGoogle Scholar
  5. 5.
    Xiao, X., Yao, Y., Zhong, W.J., Li, Y.L., Xie, Y.M.: Enhancing teleportation of quantum Fisher information by partial measurements. Phys. Rev. A. 93(1), 012307 (2016)Google Scholar
  6. 6.
    Fisher, R.A.: Theory of statistical estimation. Math. Proc. Camb. Philos. Soc. 22(5), 700–725 (1925)ADSCrossRefGoogle Scholar
  7. 7.
    Zheng, Q., Yao, Y., Li, Y.: Optimal quantum channel estimation of two interacting qubit subject to decoherence. Eur. Phys. J. D. 68, 170 (2014)Google Scholar
  8. 8.
    Ozaydin, F.: Quantum Fisher information of W States in Decoherence channels. Phys. Lett. A. 378(43), 3161–3164 (2014)Google Scholar
  9. 9.
    Li, Y.L., Xiao, X., Yao, Y.: Classical-driving-enhanced parameter-estimation precision of a non-Markovian dissipative two-state system. Phys. Rev. A. 91(5), 052105 (2015)Google Scholar
  10. 10.
    Stefanatos, D.: Optimal shortcuts to adiabaticity for a quantum piston. Automatica. 49(10), 3079–3083 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Dong, D., Petersen, I.R.: Sliding mode control of quantum systems. New J. Phys. 11(10), 105033 (2009)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Ji, Y.H., Hu, J.J., Ke, Q.: Lyapunov-based states transfer for open system with superconducting qubits. Int. J. Control. Autom. Syst. 16(1), 55–61 (2018)CrossRefGoogle Scholar
  13. 13.
    Kuang, S., Cong, S.: Lyapunov control methods of closed quantum systems. Automatica. 44(1), 98–108 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    James, M.R.: Risk-sensitive optimal control of quantum systems. Phys. Rev. A. 69(3), 032108 (2004)Google Scholar
  15. 15.
    Gammelmark, S., Molmer, K.: Bayesian parameter inference from continuously monitored quantum systems. Phys. Rev. A. 87(3), 032115 (2013)Google Scholar
  16. 16.
    Yamamoto, N.: Parametrization of the feedback Hamiltonian realizing a pure steady state. Phys. Rev. A. 72(2), 024104 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    Zhang, J., Wu, R.B., Li, C.W., Tarn, T.J.: Protecting coherence and entanglement by feedback controls. IEEE Transactions on Automation Control. 55(3), 619–633 (2010)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Qi, B., Pan, H., Guo, L.: Further results on stabilizing control of quantum systems. IEEE Trans. Autom. Control. 58(5), 1349–1354 (2013)CrossRefGoogle Scholar
  19. 19.
    Zhang, J., Liu, Y.X., Wu, R.B., Jacobs, K., Nori, F.: Quantum feedback: theory, experiments, and applications. Phys. Rep. 679, 1–60 (2017)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Mirrahimi, M., Handel, R.V.: Stabilizing feedback controls for quantum systems. SIAM J. Control. Optim. 46(2), 445–467 (2007)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Let. 72(22), 3439–3443 (1994)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Dittmann, J.: Explicit formulae for the Bures metric. J. Phys. A. 32(14), 2663–2667 (1999)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhong, W., Sun, Z., Ma, J., Wang, X.G., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A. 87(2), 022337 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    Berrada, K.: Non-Markovian Effect on the Precision of Parameter Estimation. Phys. Rev. A. 88(3), 035806 (2013)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Fuzhou Normal College of East China University of TechnologyFuzhouChina

Personalised recommendations