Skip to main content
SpringerLink
Log in

Enhancing precision of damping rate by PT symmetric Hamiltonian

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We utilize quantum Fisher information to investigate the damping parameter precision of a dissipative qubit. PT symmetric non-Hermitian Hamiltonian is used to enhance the parameter precision in two models: one is direct PT symmetric quantum feedback; the other is that the damping rate is encoded into a effective PT symmetric non-Hermitian Hamiltonian conditioned on the absence of decay events. We find that compared with the case without feedback and with Hermitian quantum feedback, direct PT symmetric non-Hermitan quantum feedback can obtain better precision of damping rate. And in the second model, the result shows that the uncertainty of damping rate can be close to 0 at the exceptional point. We also obtain that non-maximal multiparticle entanglement can improve the precision to reach Heisenberg limit.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Giovannetti, V., Lloyd, S., Maccone, L.: Metrology, quantum. Phys. Rev. Lett. 96, 010401 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  2. Giovanetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330 (2004)

    Article  ADS  Google Scholar 

  3. Xie, D., Wang, A.: Quantum metrology in correlated environments. Phys. Lett. A 378, 2079 (2014)

    Article  ADS  Google Scholar 

  4. Hinkley, N., Sherman, J.A., Phillips, N.B., Schioppo, M., Lemke, N.D., Beloy, K., Pizzocaro, M., Oates, C.W., Ludlow, A.D.: An atomic clock with \(10^{-18}\) Instabilityi. Science 341, 1215 (2013)

    Article  ADS  Google Scholar 

  5. Giovannetti, V., Lloyd, S., Maccone, L.: Advances in quantum metrology. Nat. Photon. 5, 222 (2011)

    Article  ADS  Google Scholar 

  6. Bongs, K., Launay, R., Kasevich, M.A.: High-order inertial phase shifts for time-domain atom interferometers. Appl. Phys. B 84, 599 (2006)

    Article  ADS  Google Scholar 

  7. Carlton, P.M., Boulanger, J., Kervrann, C., Sibarita, J.-B., Salamero, J., Gordon-Messer, S., Bressan, D., Haber, J.E., Haase, S., Shao, L., et al.: Fast live simultaneous multiwavelength four-dimensional optical microscopy. Proc. Natl. Acad. Sci. 107, 16016 (2010)

    Article  ADS  Google Scholar 

  8. Taylor, M.A., Janousek, J., Daria, V., Knittel, J., Hage, B., Bachor, H.-A., Bowen, W.P.: Biological measurement beyond the quantum limit. Nat. Photon. 7, 229 (2013)

    Article  ADS  Google Scholar 

  9. Abadie, J., et al.: A gravitational wave observatory operating beyond the quantum shot-noise limit. Nat. Phys. 7, 962 (2011)

    Article  Google Scholar 

  10. Aasi, J., et al.: Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613 (2013)

    Article  ADS  Google Scholar 

  11. 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 (2008)

    Article  Google Scholar 

  12. Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic, New York (1976)

    MATH  Google Scholar 

  13. Braunstein, S.L., Caves, C.M.: Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  14. Caves, C.M.: Quantum-mechanical noise in an interferometer. Phys. Rev. D 23, 1693 (1981)

    Article  ADS  Google Scholar 

  15. Lu, X.M., Wang, X.G., Sun, C.P.: Quantum Fisher information flow and non-Markovian processes of open systems. Phys. Rev. A 82, 042103 (2010)

    Article  ADS  Google Scholar 

  16. Salvatori, G., Mandarino, A., Paris, M.G.A.: Quantum metrology in Lipkin–Meshkov–Glick critical systems. Phys. Rev. A 90, 022111 (2014)

    Article  ADS  Google Scholar 

  17. 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, 3865 (1997)

    Article  ADS  Google Scholar 

  18. Wineland, D.J., Bollinger, J.J., Itano, W.M., Heinzen, D.J.: Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67 (1994)

    Article  ADS  Google Scholar 

  19. Dorner, U., Demkowicz-Dobrzanski, R., Smith, B.J., Lundeen, J.S., Wasilewski, W., Banaszek, K., Walmsley, I.A.: Optimal quantum phase estimation. Phys. Rev. Lett. 102, 040403 (2009)

    Article  ADS  Google Scholar 

  20. Dorner, U.: Quantum frequency estimation with trapped ions and atoms. New J. Phys. 14, 043011 (2012)

    Article  ADS  Google Scholar 

  21. Watanabe, Y., Sagawa, T., Ueda, M.: Optimal measurement on noisy quantum systems. Phys. Rev. Lett. 104, 020401 (2010)

    Article  ADS  Google Scholar 

  22. Tan, Q.S., Huang, Y.X., Yin, X.L., Kuang, L.M., Wang, X.G.: Enhancement of parameter-estimation precision in noisy systems by dynamical decoupling pulses. Phys. Rev. A 87, 032102 (2013)

    Article  ADS  Google Scholar 

  23. Berrada, K.: Non-Markovian effect on the precision of parameter estimation. Phys. Rev. A 88, 035806 (2013)

    Article  ADS  Google Scholar 

  24. Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum metrology in non-Markovian environments. Phys. Rev. Lett. 109, 233601 (2012)

    Article  ADS  Google Scholar 

  25. Vidrighin, M.D., Donati, G., Genoni, M.G., Jin, X.M., Kolthammer, W.S., Kim, M.S., Datta, A., Barbieri, M., Walmsley, I.A.: Joint estimation of phase and phase diffusion for quantum metrology. Nat. Commun. 5, 3532 (2014)

    Article  Google Scholar 

  26. Xie, D., Chunling, X., Wang, A.: Optimal quantum thermometry by dephasing. Quantum Inf. Process. 16, 155 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  27. Zheng, Q., Ge, L., Yao, Y., Zhi, Q.-J.: Enhancing parameter precision of optimal quantum estimation by direct quantum feedback. Phys. Rev. A 91, 033805 (2015)

    Article  ADS  Google Scholar 

  28. Ji, Y.Q., Qin, M., Shao, X.Q., Yi, X.X.: Enhanced exciton transmission by quantum-jump-based feedback. Phys. Rev. A 96, 043815 (2017)

    Article  ADS  Google Scholar 

  29. Ma, S.-Q., Zhu, H.-J., Zhang, G.: The effects of different quantum feedback operator types on the parameter precision of detection efficiency in optimal quantum estimation (2017). arXiv:1702.06229

  30. Schäfermeier, C., Kerdoncuff, H., Hoff, U.B., Fu, H., Huck, A., Bilek, J., Harris, G.I., Bowen, W.P., Gehring, T., Andersen, U.L.: Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light. Nat. Commun. 7, 13628 (2016)

    Article  ADS  Google Scholar 

  31. Mazzucchi, G., Caballero-Benitez, S.F., Ivanov, D.A., Mekhov, I.B.: Quantum optical feedback control for creating strong correlations in many-body systems. Optica 3(11), 1213–1219 (2016)

    Article  Google Scholar 

  32. Lee, T.E., Reiter, F., Moiseyev, N.: Entanglement and spin squeezing in non-Hermitian phase transitions. Phys. Rev. Lett. 113, 250401 (2014)

    Article  ADS  Google Scholar 

  33. Hou, Tie-Jun: Quantum Fisher information and spin squeezing of the non-Hermitian one-axis twisting model and the effect of dephasing. Phys. Rev. A 95, 013824 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  34. Dittmann, J.: Explicit formulae for the Bures metric. J. Phys. A 32, 2663 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  35. Zhong, W., Sun, Z., Ma, J., Wang, X.G., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A 87, 022337 (2013)

    Article  ADS  Google Scholar 

  36. Carvalho, A.R.R., Hope, J.J.: Stabilizing entanglement by quantum-jump-based feedback. Phys. Rev. A 76, 010301(R) (2007)

    Article  ADS  MathSciNet  Google Scholar 

  37. Carvalho, A.R.R., Reid, A.J.S., Hope, J.J.: Controlling entanglement by direct quantum feedback. Phys. Rev. A 78, 012334 (2008)

    Article  ADS  Google Scholar 

  38. Li, J.G., Zou, J., Shao, B., Cai, J.F.: Steady atomic entanglement with different quantum feedbacks. Phys. Rev. A 77, 012339 (2008)

    Article  ADS  Google Scholar 

  39. Wang, L.C., Huang, X.L., Yi, X.X.: Effect of feedback on the control of a two-level dissipative quantum system. Phys. Rev. A 78, 052112 (2008)

    Article  ADS  Google Scholar 

  40. Li, Y., Luo, B., Guo, H.: Entanglement and quantum discord dynamics of two atoms under practical feedback control. Phys. Rev. A 84, 012316 (2011)

    Article  ADS  Google Scholar 

  41. Yan, Y., Zou, J., Xu, B.-M., Li, J.G., Shao, B.: Measurement-based direct quantum feedback control in an open quantum system. Phys. Rev. A 88, 032320 (2013)

    Article  ADS  Google Scholar 

  42. Huang, S.Y., Goan, H.S., Li, X.Q., Milburn, G.J.: Generation and stabilization of a three-qubit entangled W state in circuit QED via quantum feedback control. Phys. Rev. A 88, 062311 (2013)

    Article  ADS  Google Scholar 

  43. Sun, H.Y., Shu, P.L., Li, C., Yi, X.X.: Feedback control on geometric phase in dissipative two-level systems. Phys. Rev. A 79, 022119 (2009)

    Article  ADS  Google Scholar 

  44. Rüter, C.E., Makris, K.G., El-Ganainy, R., Christodoulides, D.N., Segev, M., Kip, D.: Observation of parityCtime symmetry in optics. Nat. Phys. 6, 192 (2010)

    Article  Google Scholar 

  45. Gao, T., Estrecho, E., Bliokh, K.Y., Liew, T.C.H., Fraser, M.D., Brodbeck, S., Kamp, M., Schneider, C., Höfling, S., Yamamoto, Y., Nori, F., Kivshar, Y.S., Truscott, A.G., Dall, R.G., Ostrovskaya, E.A.: Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard. Nature (London) 526, 554 (2015)

    Article  ADS  Google Scholar 

  46. Liu, Z.-P., Zhang, J., Özdemir, S.K., Peng, B., Jing, H., Lü, X.-Y., Li, C.-W., Yang, L., Nori, F., Liu, Y-x: Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition. Phys. Rev. Lett 117, 110802 (2016)

    Article  ADS  Google Scholar 

  47. Li, J., Harter, A.K., Liu, J., de Melo, L., Joglekar, Y.N., Luo, L.: Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms (2016). hyperimagehttp://arxiv.org/abs/1608.05061arXiv:1608.05061

  48. Tang, J.-S., Wang, Y.T., Yu, S., He, D.Y., Xu, J.S., Liu, B.H., Chen, G., Sun, Y.N., Sun, K., Han, Y.J., Li, C.-F., Guo, G.-G.: Experimental investigation of the no-signalling principle in parity-time symmetric theory using an open quantum system. Nat. Photon. 10, 642 (2016)

    Article  ADS  Google Scholar 

  49. Wiersig, J.: Sensors operating at exceptional points: general theory. Phys. Rev. A 93, 033809 (2016)

    Article  ADS  Google Scholar 

  50. Kawabata, K., Ashida, Y., Ueda, M.: Information retrieval and criticality in parity-time-symmetric systems. Phys. Rev. Lett. 119, 190401 (2017)

    Article  ADS  Google Scholar 

  51. Dorje, C.: Brody and Eva-Maria Graefe, Mixed-State evolution in the presence of gain and loss. Phys. Rev. Lett. 109, 230405 (2012)

    Article  Google Scholar 

  52. Li, J., Liu, J., Xu, W., de Melo, L., Luo, L.: Parametric cooling of a degenerate Fermi gas in an optical trap. Phys. Rev. A 93, 041401 (2016). (R)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This research was supported by the National Natural Science Foundation of China under Grant No. 11747008 and Guangxi Natural Science Foundation 2016GXNSFBA380227.

Author information

Authors and Affiliations

  1. College of Science, Guilin University of Aerospace Technology, Guilin, Guangxi, People’s Republic of China

    Dong Xie & Chunling Xu

Authors
  1. Dong Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunling Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dong Xie.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xie, D., Xu, C. Enhancing precision of damping rate by PT symmetric Hamiltonian. Quantum Inf Process 18, 86 (2019). https://doi.org/10.1007/s11128-019-2203-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2203-z

Keywords

Search

Navigation