Skip to main content

Advertisement

Springer Nature Link
Log in

Bidirectional quantum controlled teleportation in multi-hop networks: a generalized protocol for the arbitrary n-qubit state through the noisy channel

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

This paper introduces a bidirectional quantum controlled teleportation (BQCT) protocol within a multi-hop communication network, designed to teleport an arbitrary \(n\)-qubit state through an \(m\)-hop network framework. Utilizing the IBM Quantum (IBMQ) Experience simulation framework and the Qiskit library, we empirically substantiate the protocol's efficacy. Our findings indicate consistent teleportation across varying hop counts, though the precision of the output state diminishes with an increase in hops. This research further delves into the impact of quantum noise—namely amplitude-damping, phase-damping, bit-flip, and phase-flip—on the protocol's performance. A significant finding is that the detrimental effects of quantum noise escalate with the number of hops, with noise influence showing independence from the input state and causing an exponential decrease in output state fidelity. Thus, our analysis suggests a potential for optimizing real quantum communication systems through a balance between error reduction strategies and the maximum tolerable noise level.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

The codes that support the plots within the paper are publicly available on a GitHub repository at: https://github.com/YousefMafi96/Papers/tree/Quantum-Communication.

References

  1. Du, F.F., Fan, G., Ren, X.M., Ma, M.: Deterministic hyperparallel control gates with weak Kerr effects. Adv. Quantum Technol. 6(10), 2300201 (2023). https://doi.org/10.1002/qute.202300201

    Article  Google Scholar 

  2. Du, F.F., Ren, X.M., Fan, Z.G., Li, L.H., Du, X.S., Ma, M., Fan, G., Guo, J.: Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates. Opt. Express 32(2), 1686–1700 (2024). https://doi.org/10.1364/OE.508088

    Article  ADS  Google Scholar 

  3. Du, F.F., Ren, X.M., Ma, M., Fan, G.: Qudit-based high-dimensional controlled-not gate. Opt. Lett. 49(5), 1229–1232 (2024). https://doi.org/10.1364/OL.518336

    Article  ADS  Google Scholar 

  4. Du, F.F., Fan, G., Ren, X.M.: Kerr-effect-based quantum logical gates in decoherence-free subspace. Quantum 8, 1342 (2024). https://doi.org/10.22331/q-2024-05-13-1342

    Article  Google Scholar 

  5. Gisin, N., Thew, R.: Quantum communication. Nat. Photonics 1, 165–171 (2007). https://doi.org/10.1038/nphoton.2007.22

    Article  ADS  Google Scholar 

  6. Mafi, Y., Kazemikhah, P., Ahmadkhaniha, A., Aghababa, H., Kolahdouz, M.: Bidirectional quantum teleportation of an arbitrary number of qubits over a noisy quantum system using 2 n Bell states as quantum channel. Opt. Quant. Electron. 54, 568 (2022). https://doi.org/10.1007/s11082-022-03951-x

    Article  Google Scholar 

  7. Ahmadkhaniha, A., Mafi, Y., Kazemikhah, P., Aghababa, H., Barati, M., Kolahdouz, M.: Enhancing quantum teleportation: an enable-based protocol exploiting distributed quantum gates. Opt. Quant. Electron. 55, 1079 (2023). https://doi.org/10.1007/s11082-023-05351-1

    Article  Google Scholar 

  8. Mafi, Y., Kazemikhah, P., Ahmadkhaniha, A., Aghababa, H., Kolahdouz, M.: Efficient controlled quantum broadcast protocol using 6n-qubit cluster state in noisy channels. Opt. Quant. Electron. 55, 653 (2023). https://doi.org/10.1007/s11082-023-04928-0

    Article  Google Scholar 

  9. Mafi, Y., Kookani, A., Aghababa, H., Barati, M., Kolahdouz, M.: Quantum broadcasting of the generalized GHZ state: quantum noise analysis using quantum state tomography via IBMQ simulation. Phys. Scr. 99, 085124 (2024). https://doi.org/10.1088/1402-4896/ad62a9

    Article  Google Scholar 

  10. Khorrampanah, M., Houshmand, M., Sadeghizadeh, M., Aghababa, H., Mafi, Y.: Enhanced multiparty quantum secret sharing protocol based on quantum secure direct communication and corresponding qubits in noisy environment. Opt. Quant. Electron. 54, 832 (2022). https://doi.org/10.1007/s11082-022-04164-y

    Article  Google Scholar 

  11. Zhou, L., Sheng, Y.B.: One-step device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron. 65(5), 250311 (2022). https://doi.org/10.1007/s11433-021-1863-9

    Article  ADS  MathSciNet  Google Scholar 

  12. Zhou, L., Sheng, Y.B., Long, G.L.: Device-independent quantum secure direct communication against collective attacks. Sci. Bull. 65(1), 12–20 (2020). https://doi.org/10.1016/j.scib.2019.10.025

    Article  Google Scholar 

  13. Zhou, L., Xu, B.W., Zhong, W., Sheng, Y.B.: Device-independent quantum secure direct communication with single-photon sources. Phys. Rev. Appl. 19(1), 014036 (2023). https://doi.org/10.1103/PhysRevApplied.19.014036

    Article  ADS  Google Scholar 

  14. Guo, R., Zhou, L., Gu, S.P., Wang, X.F., Sheng, Y.B.: Generation of concatenated Greenberger–Horne–Zeilinger-type entangled coherent state based on linear optics. Quantum Inf. Process. 16, 1–13 (2017). https://doi.org/10.1007/s11128-017-1519-9

    Article  ADS  MathSciNet  Google Scholar 

  15. Zhou, L., Ou-Yang, Y., Wang, L., Sheng, Y.B.: Protecting single-photon entanglement with practical entanglement source. Quantum Inf. Process. 16, 1–21 (2017). https://doi.org/10.1007/s11128-017-1601-3

    Article  ADS  MathSciNet  Google Scholar 

  16. Zarmehi, F., Kochakzadeh, M.H., Abbasi-Moghadam, D., Talebi, S.: Efficient circular controlled quantum teleportation and broadcast schemes in the presence of quantum noises. Quantum Inf. Process. 20, 175 (2021). https://doi.org/10.1007/s11128-021-03088-y

    Article  ADS  MathSciNet  Google Scholar 

  17. Zha, X.-W., Zou, Z.-C., Qi, J.-X., Song, H.-Y.: Bidirectional quantum controlled teleportation via five-qubit cluster state. Int. J. Theor. Phys. 52, 1740–1744 (2013). https://doi.org/10.1007/s10773-012-1208-5

    Article  MathSciNet  Google Scholar 

  18. Shukla, C., Banerjee, A., Pathak, A.: Bidirectional controlled teleportation by using 5-qubit states: a generalized view. Int. J. Theor. Phys. 52, 3790–3796 (2013). https://doi.org/10.1007/s10773-013-1684-2

    Article  Google Scholar 

  19. Verma, V.: Bidirectional controlled quantum teleportation of multi-qubit entangled states via five-qubit entangled state. Phys. Scr. 96, 035105 (2021). https://doi.org/10.1088/1402-4896/abd78f

    Article  ADS  Google Scholar 

  20. Yan, A.: Bidirectional controlled teleportation via six-qubit cluster state. Int. J. Theor. Phys. 52, 3870–3873 (2013). https://doi.org/10.1007/s10773-013-1694-0

    Article  MathSciNet  Google Scholar 

  21. Sun, X.M., Zha, X.W.: A scheme of bidirectional quantum controlled teleportation via six-qubit maximally entangled state. Acta Photonica Sin. 48, 1052–1056 (2013)

    Google Scholar 

  22. Chen, Y.: Bidirectional quantum controlled teleportation by using a genuine six-qubit entangled state. Int. J. Theor. Phys. 54, 269–272 (2015). https://doi.org/10.1007/s10773-014-2221-7

    Article  Google Scholar 

  23. Li, Y.-H., Nie, L.-P., Li, X.-L., Sang, M.-H.: Asymmetric bidirectional controlled teleportation by using six-qubit cluster state. Int. J. Theor. Phys. 55, 3008–3016 (2016). https://doi.org/10.1007/s10773-016-2933-y

    Article  Google Scholar 

  24. Nie, Y.-Y., Sang, M.-H.: Effects of noise on asymmetric bidirectional controlled teleportation. Int. J. Theor. Phys. 55, 4759–4765 (2016). https://doi.org/10.1007/s10773-016-3099-3

    Article  Google Scholar 

  25. Sang, M.-H.: Bidirectional quantum controlled teleportation by using a seven-qubit entangled state. Int. J. Theor. Phys. 55, 380–383 (2016). https://doi.org/10.1007/s10773-015-2670-7

    Article  Google Scholar 

  26. Duan, Y.-J., Zha, X.-W., Sun, X.-M., Xia, J.-F.: Bidirectional quantum controlled teleportation via a maximally seven-qubit entangled state. Int. J. Theor. Phys. 53, 2697–2707 (2014). https://doi.org/10.1007/s10773-014-2065-1

    Article  Google Scholar 

  27. Zhang, D., Zha, X.-W., Duan, Y.-J.: Bidirectional and asymmetric quantum controlled teleportation. Int. J. Theor. Phys. 54, 1711–1719 (2015). https://doi.org/10.1007/s10773-014-2372-6

    Article  Google Scholar 

  28. Nie, Y.-Y., Sang, M.-H.: Asymmetric bidirectional controlled teleportation via seven-photon entangled state. Int. J. Theor. Phys. 56, 3452–3454 (2017). https://doi.org/10.1007/s10773-017-3510-8

    Article  MathSciNet  Google Scholar 

  29. Wu, H., Zha, X.-W., Yang, Y.-Q.: Controlled bidirectional hybrid of remote state preparation and quantum teleportation via seven-qubit entangled state. Int. J. Theor. Phys. 57, 28–35 (2018). https://doi.org/10.1007/s10773-017-3537-x

    Article  Google Scholar 

  30. Wang, J.-W., Shu, L.: Bidirectional quantum controlled teleportation of qudit state via partially entangled GHZ-type states. Int. J. Mod. Phys. B 29, 1550122 (2015). https://doi.org/10.1142/S0217979215501222

    Article  ADS  MathSciNet  Google Scholar 

  31. Ma, P.-C., Chen, G.-B., Li, X.-W., Zhan, Y.-B.: Bidirectional controlled quantum teleportation in the three-dimension system. Int. J. Theor. Phys. 57, 2233–2240 (2018). https://doi.org/10.1007/s10773-017-3510-8

    Article  MathSciNet  Google Scholar 

  32. Zhang, D., Zha, X.W., Li, W., Yu, Y.: Bidirectional and asymmetric quantum controlled teleportation via maximally eight-qubit entangled state. Quantum Inf. Process. 14, 3835–3844 (2015). https://doi.org/10.1007/s11128-015-1067-0

    Article  ADS  MathSciNet  Google Scholar 

  33. Huo, G., Zhang, T., Zha, X., Zhang, X., Zhang, M.: Controlled asymmetric bidirectional quantum teleportation of two-and three-qubit states. Quantum Inf. Process. 20, 1–11 (2021). https://doi.org/10.1007/s11128-020-02956-3

    Article  MathSciNet  Google Scholar 

  34. Jiang, Y.-L., Zhou, R.-G., Hao, D.-Y., Hu, W.: Bidirectional controlled quantum teleportation of three-qubit state by a new entangled eleven-qubit state. Int. J. Theor. Phys. 60, 3618–3630 (2021). https://doi.org/10.1007/s10773-021-04935-5

    Article  MathSciNet  Google Scholar 

  35. Kazemikhah, P., Tabalvandani, M.B., Mafi, Y., Aghababa, H.: Asymmetric bidirectional controlled quantum teleportation using eight qubit cluster state. Int. J. Theor. Phys. 61, 17 (2022). https://doi.org/10.1007/s10773-022-04995-1

    Article  MathSciNet  Google Scholar 

  36. Yu, X.-T., Xu, J., Zhang, Z.-C.: Distributed wireless quantum communication networks. Chin. Phys. B 22, 090311 (2013). https://doi.org/10.1088/1674-1056/22/9/090311

    Article  ADS  Google Scholar 

  37. Yu, X.-T., Zhang, Z.-C., Xu, J.: Distributed wireless quantum communication networks with partially entangled pairs. Chin. Phys. B 23, 010303 (2013). https://doi.org/10.1088/1674-1056/23/1/010303

    Article  Google Scholar 

  38. Cai, X.-F., Yu, X.-T., Shi, L.-H., Zhang, Z.-C.: Partially entangled states bridge in quantum teleportation. Front. Phys. 9, 646–651 (2014). https://doi.org/10.1007/s11467-014-0432-2

    Article  ADS  Google Scholar 

  39. Shi, L.-H., Yu, X.-T., Cai, X.-F., Gong, Y.-X., Zhang, Z.-C.: Quantum information transmission in the quantum wireless multi-hop network based on Werner state. Chin. Phys. B 24, 050308 (2015). https://doi.org/10.1088/1674-1056/24/5/050308

    Article  ADS  Google Scholar 

  40. Yang, Y.-G., Cao, S.-N., Zhou, Y.-H., Shi, W.-M.: Quantum wireless network communication based on cluster states. Mod. Phys. Lett. A 35, 2050178 (2020). https://doi.org/10.1142/S0217732320501783

    Article  ADS  MathSciNet  Google Scholar 

  41. Zou, Z.-Z., Yu, X.-T., Gong, Y.-X., Zhang, Z.-C.: Multi-hop teleportation of two-qubit state via the composite GHZ–Bell channel. Phys. Lett. A 381, 76–81 (2017). https://doi.org/10.1016/j.physleta.2016.10.048

    Article  ADS  Google Scholar 

  42. Yang, Y.-L., Yang, Y.-G., Zhou, Y.-H., Shi, W.-M., Li, J.: Efficient quantum multi-hop communication based on Greenberger–Horne–Zeilinger states and Bell states. Quantum Inf. Process. 20, 189 (2021). https://doi.org/10.1007/s11128-021-03121-0

    Article  ADS  MathSciNet  Google Scholar 

  43. Zhang, Z., Wang, J., Sun, M.: Multi-hop teleportation via the composite of asymmetric W state and Bell state. Int. J. Theor. Phys. 57, 3605–3620 (2018). https://doi.org/10.1007/s10773-018-3874-4

    Article  Google Scholar 

  44. Choudhury, B.S., Samanta, S.: A multi-hop teleportation protocol of arbitrary four-qubit states through intermediate nodes. International Journal of Quantum Information. 16, 1850026 (2018). https://doi.org/10.1142/S0219749918500260

    Article  ADS  MathSciNet  Google Scholar 

  45. Wu, F., Bai, M.-Q., Tang, L., Mo, Z.-W.: Multi-hop quantum teleportation of an arbitrary two-qubit state based on hierarchical simultaneous entanglement swapping. J. Phys. A: Math. Theor.. 56, 065301 (2023). https://doi.org/10.1088/1751-8121/acb91d

    Article  ADS  MathSciNet  Google Scholar 

  46. Zhang, Z., Sang, Y.: Bidirectional quantum teleportation in multi-hop communication network. Quantum Inf. Process. 22, 201 (2023). https://doi.org/10.1007/s11128-023-03950-1

    Article  ADS  MathSciNet  Google Scholar 

  47. Qiskit: An Open-source Framework for Quantum Computing. (2023). Url: https://ibm.com/quantum/qiskit.

  48. Guérin, P.A., Rubino, G., Brukner, Č: Communication through quantum-controlled noise. Phys. Rev. A 99, 062317 (2019). https://doi.org/10.1103/PhysRevA.99.062317

    Article  ADS  Google Scholar 

  49. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press (2001)

    Google Scholar 

  50. Braunstein, S.L.: Quantum error correction for communication with linear optics. Nature 394, 47–49 (1998). https://doi.org/10.1038/27850

    Article  ADS  Google Scholar 

Download references

Acknowledgements

No acknowledgments.

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran

    Yousef Mafi, Ali Kookani & Mohammadreza Kolahdouz

  2. Department of Engineering, Loyola University Maryland, Maryland, USA

    Hossein Aghababa

  3. Swanson School of Engineering, Electrical Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Masoud Barati

  4. Quantum Computation and Communication Laboratory (QCCL), University of Tehran, Tehran, Iran

    Yousef Mafi & Ali Kookani

  5. Founder of Quantum Computation and Communication Laboratory (QCCL), University of Tehran, Tehran, Iran

    Hossein Aghababa

Authors
  1. Yousef Mafi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Ali Kookani
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Hossein Aghababa
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Masoud Barati
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Mohammadreza Kolahdouz
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

Y. M. contributed to conceptualization, methodology, investigation, implementation, noise analysis, and visualization. A. K. contributed to software, formal analysis, validation, literature survey, writing, data curation, and visualization. H. A. performed project administration, validation, and supervision. M. B. and M. K. performed validation and supervision.

Corresponding author

Correspondence to Hossein Aghababa.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Ethical approval

The authors ethically approve the material of the paper. Authors have been informed and consent regarding the submission of the article. No human/animal has participated in this research.

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

Mafi, Y., Kookani, A., Aghababa, H. et al. Bidirectional quantum controlled teleportation in multi-hop networks: a generalized protocol for the arbitrary n-qubit state through the noisy channel. Quantum Inf Process 23, 350 (2024). https://doi.org/10.1007/s11128-024-04561-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-024-04561-0

Keywords