Skip to main content
Log in

Optimal tripartite quantum teleportation protocol through noisy channels

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper we propose a tripartite teleportation protocol to teleport an unknown quantum state via noisy quantum channels with fidelity equal to one even with a non-maximally entangled state. In our protocol we utilize environment-assisted measurement during entanglement distribution and further modify the standard teleportation protocol to apply weak measurement reversal in the last step of teleportation. We design the weak measurement reversal operators to make the teleportation fidelity equal to one, independent of the magnitude of decoherence or the shared entangled state parameters. Since the teleportation fidelity is always equal to one, we can optimize the teleportation success probability without affecting the fidelity. Moreover, we give the detailed procedure of the standard tripartite teleportation protocol in the presence of amplitude damping and derive the final expression of the average standard teleportation fidelity.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data availability and materials

Not applicable. For all requests relating to the paper, please contact the first author.

References

  1. 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, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Shi, B.S., Tomita, A.: Teleportation of an unknown state by W state. Phys. Lett. Sect. A Gen. At. Solid State Phys. 296, 161–164 (2002). https://doi.org/10.1016/S0375-9601(02)00257-8

    Article  ADS  MATH  Google Scholar 

  3. Bartlett, S.D., Munro, W.J.: Quantum teleportation of optical quantum gates. Phys. Rev. Lett. 90, 117901 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A. 58, 4394 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  5. Zounia, M., Shamirzaie, M., Ashouri, A.: Quantum teleportation via noisy bipartite and tripartite accelerating quantum states: beyond the single mode approximation. J. Phys. A Math. Theor. 50, 395302 (2017). https://doi.org/10.1088/1751-8121/aa812b

    Article  MathSciNet  MATH  Google Scholar 

  6. Guan, S.Y., Jin, Z., Wu, H.J., Zhu, A.D., Wang, H.F., Zhang, S.: Restoration of three-qubit entanglements and protection of tripartite quantum state sharing over noisy channels via environment-assisted measurement and reversal weak measurement. Quantum Inf. Process. 16, 1–15 (2017). https://doi.org/10.1007/s11128-017-1584-0

    Article  ADS  MATH  Google Scholar 

  7. Kumar, S.A.: Quantum teleportation of a tripartite entangled coherent state. Mod. Phys. Lett. A. 36, 2150217 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Bhatia, P.S.: Elementary tripartite quantum communication photonic network at the telecom wavelength. Laser Phys. 31, 95203 (2021)

    Article  Google Scholar 

  9. Joy, D., Sabir, M.: Efficient schemes for the quantum teleportation of a sub-class of tripartite entangled states. Quantum Inf. Process. 17, 1–11 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fedrizzi, A., Ursin, R., Herbst, T., Nespoli, M., Prevedel, R., Scheidl, T., Tiefenbacher, F., Jennewein, T., Zeilinger, A.: High-fidelity transmission of entanglement over a high-loss free-space channel. Nat. Phys. 5, 389–392 (2009)

    Article  Google Scholar 

  11. Gyongyosi, L., Imre, S.: Entanglement concentration service for the quantum Internet. Quantum Inf. Process. 19, 1–28 (2020)

    MathSciNet  MATH  Google Scholar 

  12. Jiang, L., Taylor, J.M., Nemoto, K., Munro, W.J., Van Meter, R., Lukin, M.D.: Quantum repeater with encoding. Phys. Rev. A. 79, 32325 (2009)

    Article  ADS  Google Scholar 

  13. Yi, X.-F., Xu, P., Yao, Q., Quan, X.: Quantum repeater without Bell measurements in double-quantum-dot systems. Quantum Inf. Process. 18, 82 (2019)

    Article  ADS  MATH  Google Scholar 

  14. Behera, B.K., Seth, S., Das, A., Panigrahi, P.K.: Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer. Quantum Inf. Process. 18, 1–13 (2019)

    MATH  Google Scholar 

  15. Harraz, S., Cong, S., Member, S., Nieto, J.J.: Protected quantum teleportation through noisy channel by weak measurement and environment-assisted measurement. IEEE Commun. Lett. 26(3), 528–531 (2022). https://doi.org/10.1109/LCOMM.2021.3138854

  16. Jung, E., Hwang, M.-R., Park, D., Tamaryan, S.: Three-party entanglement in tripartite teleportation scheme through noisy channels. Quantum Inf. Comput. 10, 377–397 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Yamamoto, T., Koashi, M., Özdemir, ŞK., Imoto, N.: Experimental extraction of an entangled photon pair from two identically decohered pairs. Nature 421, 343–346 (2003)

    Article  ADS  Google Scholar 

  18. Li, M., Fei, S.-M., Li-Jost, X.: Quantum entanglement: separability, measure, fidelity of teleportation, and distillation. Math. Phys, Adv (2010). https://doi.org/10.1155/2010/301072

    Book  MATH  Google Scholar 

  19. Devetak, I., Winter, A.: Distillation of secret key and entanglement from quantum states. Proc. R. Soc. A Math. Phys. Eng. Sci. 461, 207–235 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  20. Lee, S.-W., Ralph, T.C., Jeong, H.: Fundamental building block for all-optical scalable quantum networks. Phys. Rev. A. 100, 52303 (2019)

    Article  ADS  Google Scholar 

  21. Azuma, K., Tamaki, K., Lo, H.-K.: All-photonic quantum repeaters. Nat. Commun. 6, 1–7 (2015)

    Google Scholar 

  22. Dias, J., Ralph, T.C.: Quantum repeaters using continuous-variable teleportation. Phys. Rev. A. 95, 22312 (2017)

    Article  ADS  Google Scholar 

  23. Barasiński, A., Černoch, A., Lemr, K.: Demonstration of controlled quantum teleportation for discrete variables on linear optical devices. Phys. Rev. Lett. 122, 170501 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  24. Pan, J.-W., Gasparoni, S., Ursin, R., Weihs, G., Zeilinger, A.: Experimental entanglement purification of arbitrary unknown states. Nature 423, 417–422 (2003)

    Article  ADS  Google Scholar 

  25. Zhang, Q., Goebel, A., Wagenknecht, C., Chen, Y.-A., Zhao, B., Yang, T., Mair, A., Schmiedmayer, J., Pan, J.-W.: Experimental quantum teleportation of a two-qubit composite system. Nat. Phys. 2, 678–682 (2006)

    Article  Google Scholar 

  26. Im, D., Lee, C., Kim, Y., Nha, H., Kim, M.S., Lee, S.-W., Kim, Y.-H.: Optimal teleportation via noisy quantum channels without additional qubit resources. npj Quantum Inf. 7, 86 (2021). https://doi.org/10.1038/s41534-021-00426-x

    Article  ADS  Google Scholar 

  27. Lee, S.-W., Im, D.-G., Kim, Y.-H., Nha, H., Kim, M.S.: Quantum teleportation is a reversal of quantum measurement. Phys. Rev. Res. 3(3), 033119 (2021)

    Article  Google Scholar 

  28. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  29. Harraz, S., Cong, S.: Comparison of quantum state protection against decoherence, a survey. Int. J. Quantum Information, 2250007 (2022)

  30. Kim, Y.S., Lee, J.C., Kwon, O., Kim, Y.H.: Protecting entanglement from decoherence via weak quantum measurement. Pacific Rim Conf. Lasers Electro-Optics, CLEO - Tech. Dig. 8, 117–120 (2013). https://doi.org/10.1109/CLEOPR.2013.6600351

  31. Harraz, S., Cong, S.: N-qubit state protection against amplitude damping by quantum feed-forward control and its reversal. IEEE J. Sel. Top. Quantum Electron. 26, 1–8 (2020). https://doi.org/10.1109/JSTQE.2020.2969574

    Article  Google Scholar 

  32. Harraz, S., Cong, S., Li, K.: Two-qubit state recovery from amplitude damping based on weak measurement. Quantum Inf. Process. 19, 1–22 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  33. Harraz, S., Cong, S., Nieto, J.J.: Quantum state and entanglement protection in finite temperature environment by quantum feed-forward control. Eur. Phys. J. Plus. 136, 1–12 (2021). https://doi.org/10.1140/epjp/s13360-021-01861-7

    Article  Google Scholar 

  34. Wang, K., Zhao, X., Yu, T.: Environment-assisted quantum state restoration via weak measurements. Phys. Rev. At. Mol. Opt. Phys. 89, 1–6 (2014). https://doi.org/10.1103/PhysRevA.89.042320

    Article  Google Scholar 

  35. Gregoratti, M., Werner, R.F.: Quantum lost and found. J. Mod. Opt. 50–6, 915–933 (2003). https://doi.org/10.1080/09500340308234541

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Zhao, X., Hedemann, S.R., Yu, T.: Restoration of a quantum state in a dephasing channel via environment-assisted error correction. Phys. Rev. A At. Mol. Opt. Phys. 88, 1–8 (2013). https://doi.org/10.1103/PhysRevA.88.022321

    Article  Google Scholar 

  37. Wang, Q., Li, W.J.: Restoring distribution entanglement for two-qubit transmission using environment-assisted measurement and quantum measurement reversal. Laser Phys. 29, 115201 (2019). https://doi.org/10.1088/1555-6611/ab41ed

    Article  ADS  Google Scholar 

  38. Wang, Q., Xu, L., Li, W.J., He, Z.: Environment-assisted high-dimensional quantum entanglement restoration via weak measurement reversal. Laser Phys. 30, 065202 (2020). https://doi.org/10.1088/1555-6611/ab8124

    Article  ADS  Google Scholar 

  39. Li, Y.L., Sun, F., Yang, J., Xiao, X.: Enhancing the teleportation of quantum Fisher information by weak measurement and environment-assisted measurement. Quantum Inf. Process. 20, 1–19 (2021). https://doi.org/10.1007/s11128-021-02998-1

    Article  ADS  MathSciNet  Google Scholar 

  40. Cunha, M., Fonseca, A., Silva, E.O.: Tripartite entanglement: Foundations and applications. Universe. 5, 209 (2019)

    Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China under Grants 61973290 and Ministry of Science and Technology of P. R. China Program under the grant no. QN2022200007L.

Author information

Authors and Affiliations

Authors

Contributions

SH conceived and developed the idea of EA-WMR, performed the experiments and analyzed the results. SC conceived and supervised the project. JJN discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Sajede Harraz.

Ethics declarations

Conflict of interests

The authors have no competing interests to declare that are relevant to the content of this article.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Harraz, S., Cong, S. & Nieto, J.J. Optimal tripartite quantum teleportation protocol through noisy channels. Quantum Inf Process 22, 83 (2023). https://doi.org/10.1007/s11128-023-03830-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-03830-8

Keywords

Navigation