International Journal of Theoretical Physics

, Volume 53, Issue 3, pp 1056–1063 | Cite as

Error Analysis on Photonic Qubit Rotations Implemented by Wave Plates

  • Zhi-Kun Su
  • Jia-Ning Xie
  • Na Li
  • Chuan-Yun Zhu
  • Cui-Wen Ren
  • Ding-An Han


Optical Poincare sphere rotations \(e^{-i\theta\sigma_{x}/2}\), \(e^{-i\theta\sigma_{y}/2}\) and \(e^{-i\theta\sigma_{z}/2}\) can be realized by wave-plate combinations. Errors due to combinations with non-ideal wave plates are discussed for three specific combinations (θ=π) by trace distance. The result shows that different settings of combinations affect trace distance: (i) trace distance for \(e^{-i\pi\sigma_{x}/2}\) equals that for \(e^{-i\pi\sigma_{z}/2}\), but both of them are smaller than that for \(e^{-i\pi\sigma_{y}/2}\), when optics-axis random errors are considered; (ii) trace distance for \(e^{-i\pi\sigma_{x}/2}\) also equals that for \(e^{-i\pi\sigma_{z}/2}\), but both of them are larger than that for \(e^{-i\pi\sigma_{y}/2}\), when phase-shift random errors are considered. The method outlined in this paper is general and is useful to analyze other combinations.


Wave plate Unitary rotation Trace distance 



This work is supported by the Ph.D. Start-up Fund of Natural Science Foundation of Foshan University, the High-quality lesson Foundation of Foshan University (Photoelectric information and technology experiment) and the National Natural Science Foundation of China under grant no. 61307062, no. 61275059 and no. 61008063.


  1. 1.
    Wang, J., Fang, Q., Wang, Y.: Two novel polarization transformers using rotatable waveplates. Optik—Int. J. Light Electron Opt. 116(2), 93–98 (2005) CrossRefGoogle Scholar
  2. 2.
    Langford, N.K.: Encoding, manipulating and measuring quantum information in optics. Ph.D. Thesis, University of Queensland (2007) Google Scholar
  3. 3.
    Wang, J., Li, J.: Error analysis on two-waveplate polarization state transformers by geometry method. Optik—Int. J. Light Electron Optics 121(8), 711–714 (2010) CrossRefGoogle Scholar
  4. 4.
    Viola, L., Lloyd, S.: Dynamical suppression of decoherence in two-state quantum systems. Phys. Rev. A 58, 2733–2744 (1998) ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    Viola, L., Knill, E., Lloyd, S.: Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417–2421 (1999) ADSCrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Cywiński, Ł., Lutchyn, R.M., Nave, C.P., Das Sarma, S.: How to enhance dephasing time in superconducting qubits. Phys. Rev. B 77, 174509 (2008) ADSCrossRefGoogle Scholar
  7. 7.
    Biercuk, M.J., Doherty, A.C., Uys, H.: Dynamical decoupling sequence construction as a filter-design problem. J. Phys. B, At. Mol. Opt. Phys. 44(15), 154002 (2011) ADSCrossRefGoogle Scholar
  8. 8.
    Su, Z.-K., Jiang, S.-J.: Filter-design perspective applied to dynamical decoupling of a multi-qubit system. J. Phys. B, At. Mol. Opt. Phys. 45(2), 025502 (2012) ADSCrossRefGoogle Scholar
  9. 9.
    Bardhan, B.R., Anisimov, P.M., Gupta, M.K., Brown, K.L., Jones, N.C., Lee, H., Dowling, J.P.: Dynamical decoupling in optical fibers: preserving polarization qubits from birefringent dephasing. Phys. Rev. A 85, 022340 (2012) ADSCrossRefGoogle Scholar
  10. 10.
    Yan, B., Li, C.-F., Guo, G.-C.: Preserving entanglement of flying qubits in optical fibers by dynamical decoupling (2011). arXiv:1111.6670
  11. 11.
    Lucamarini, M., Di Giuseppe, G., Damodarakurup, S., Vitali, D., Tombesi, P.: Suppression of polarization decoherence for traveling light pulses via bang-bang dynamical decoupling. Phys. Rev. A 83, 032320 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    Lucamarini, M., Di Giuseppe, G., Vitali, D., Tombesi, P.: Open-loop and closed-loop control of flying qubits. J. Phys. B, At. Mol. Opt. Phys. 44(15), 154005 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    Berglund, A.J.: Quantum coherence and control in one-and two-photon optical systems (2000). arXiv:quant-ph/0010001
  14. 14.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Zhi-Kun Su
    • 1
  • Jia-Ning Xie
    • 1
  • Na Li
    • 1
  • Chuan-Yun Zhu
    • 1
  • Cui-Wen Ren
    • 1
  • Ding-An Han
    • 1
  1. 1.Department of PhysicsFoshan UniversityFoshanChina

Personalised recommendations