Evolution reconstruction of deviate Bell states by extending the novel Fourier-based method

Abstract

The time-variant quantum communication channel affected by uncontrollable environmental factors induces an unrepeatable evolution of Bell states, which calls for a universal method of evolution reconstruction. The novel Fourier-based method proposed recently is extended and demonstrated for the deviated Bell states. The density operators are represented in terms of expectation value functions of projectors. The optimal quorums and measurement schemes are presented. The ways of extending the Fourier-based recovery series are also given. The simulated results show that our method is effective and the novel Fourier-based method can keep a good performance for the evolution reconstruction of Bell states.

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References

  1. 1.

    Gross, D., Liu, Y.-K., Flammia, S.T., Becker, S., Eisert, J.: Quantum state tomography via compressed sensing. Phys. Rev. Lett. 105, 150401 (2010)

    ADS  Article  Google Scholar 

  2. 2.

    Teo, Y.S., et al.: Quantum-state reconstruction by maximizing likelihood and entropy. Phys. Rev. Lett. 107, 020404 (2011)

    ADS  Article  Google Scholar 

  3. 3.

    Lanyon, B.P., et al.: Effcient tomography of a quantum many-body system. Nat. Phys. 13, 1158–1162 (2017)

    Article  Google Scholar 

  4. 4.

    Torlai, G., Mazzola, G., Carrasquilla, J., et al.: Neural-network quantum state tomography. Nat. Phys. 14, 447–550 (2018)

    Article  Google Scholar 

  5. 5.

    Liu, Y., Tian, J., Betzholz, R., Cai, J.: Pulsed quantum state reconstruction of dark systems. Phys. Rev. Lett. 122, 110406 (2019)

    ADS  Article  Google Scholar 

  6. 6.

    Yang, P., Yu, M., Betzholz, R., Arenz, C., Cai, J.: Complete quantum-state tomography with a local random field. Phys. Rev. Lett. 124, 101103 (2020)

    Article  Google Scholar 

  7. 7.

    Gutzeit, R., Wallentowitz, S., Vogel, W.: Reconstructing the time evolution of a quantized oscillator. Phys. Rev. A 61, 062105 (2000)

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    Brune, M., Bernu, J., Guerlin, C., Deléglise, S., Sayrin, C.: Process tomography of field damping and measurement of Fock state lifetimes by quantum nondemolition photon counting in a cavity. Phys. Rev. Lett. 101, 240402 (2008)

    ADS  Article  Google Scholar 

  9. 9.

    Coffey, T.M., Wyatt, R.B., Schieve, W.C.: Reconstruction of the time-dependent wave function exclusively from position data. Phys. Rev. Lett. 107, 230403 (2011)

    Article  Google Scholar 

  10. 10.

    Ralph, J.F., Jacobs, K., Hill, C.D.: Frequency tracking and parameter estimation for robust quantum state estimation. Phys. Rev. A 84, 052119 (2011)

    ADS  Article  Google Scholar 

  11. 11.

    Sayrin, C., Dotsenko, I., Gleyzes, S., Brune, M., Raimond, J.M.: Optimal time-resolved photon number distribution reconstruction of a cavity field by maximum likelihood. New J. Phys. 14, 115007 (2012)

    ADS  Article  Google Scholar 

  12. 12.

    Ralph, J.F., Combes, J., Wiseman, H.M.: An interleaved sampling scheme for the characterization of single qubit dynamics. Quantum Inf. Process. 11, 1523–1531 (2012)

    ADS  MathSciNet  Article  Google Scholar 

  13. 13.

    Liu, Z., Cavaletto, S.M., et al.: Phase reconstruction of strong-field excited systems by transient-absorption spectroscopy. Phys. Rev. Lett. 115, 033003 (2015)

    ADS  Article  Google Scholar 

  14. 14.

    Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661–663 (1991)

    ADS  MathSciNet  Article  Google Scholar 

  15. 15.

    Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69(20), 2881–2884 (1992)

    ADS  MathSciNet  Article  Google Scholar 

  16. 16.

    Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895 (1993)

    ADS  MathSciNet  Article  Google Scholar 

  17. 17.

    Hassanpour, S., Houshmand, M.: Bidirectional teleportation of a pure EPR state by using GHZ states. Quantum Inf. Process. 15(2), 905–912 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  18. 18.

    Ma, X.-S., Herbst, T., et al.: Quantum teleportation over 143 kilometres using active feed-forward. Nature 489, 269–273 (2012)

    ADS  Article  Google Scholar 

  19. 19.

    Yu-Yang, D., Hua, C., Shuang, W., et al.: Polarization variations in installed fibers and their influence on quantum key distribution systems. Opt. Express 25(22), 29923–29936 (2017)

    Google Scholar 

  20. 20.

    Roux Filippus Stefanus: Evolution equation for multi-photon states in turbulence. J. Phys. A: Math. Theor. 52, 405301 (2019)

    MathSciNet  Article  Google Scholar 

  21. 21.

    Zhou, H., Su, Y., Wang, R., et al.: Online evolution reconstruction from a single measurement record with random time intervals for quantum communication. Quantum Inf. Process. 16, 247 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  22. 22.

    Zhou, H., Wang, A., Zhu, Y., et al.: Representing expectation values of projectors as series for evolution reconstruction. Quantum Inf. Process. 15, 5155–5165 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  23. 23.

    Steuernagel, O., Vaccaro, J.A.: Reconstructing the density operator via simple projectors. Phys. Rev. Lett. 75, 18 (1995)

    Article  Google Scholar 

  24. 24.

    Bruß, D.: Optimal Eavesdropping in quantum cryptography with six states. Phys. Rev. Lett. 81(14), 3018–3021 (1998)

    ADS  Article  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 61975238).

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Correspondence to Hua Zhou.

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Zhou, H., Li, G., Zhu, W. et al. Evolution reconstruction of deviate Bell states by extending the novel Fourier-based method. Quantum Inf Process 19, 217 (2020). https://doi.org/10.1007/s11128-020-02719-0

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Keywords

  • Evolution reconstruction
  • Bell states
  • Novel Fourier-based method
  • Projective measurement