Skip to main content
SpringerLink
Log in

Mentor Initiated Controlled Bi-directional Remote State Preparation Scheme For \((2 \iff 4)\)-Qubit Entangled States in Noisy Channel

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

In this paper we present a bi-directional protocol for mutual remote preparation of a two and a four-qubit non-maximally entangled state where the parties intending to remotely prepare the respective states are not initially entangled. There is a controller of the protocol who oversees the performances of other parties and acts to signal for the execution of the final step in the protocol. There is a Mentor whose action creates entanglement between the rest of the parties and also determines one of the several possible courses of the communication scheme. After that the Mentor quits. The effect of three different noises, namely, Bit-flip, Phase-flip and Amplitude-damping noises are analyzed using the Kraus operator on the otherwise perfect protocol. The decreased fidelity in the presence of noise is numerically studied with respect to noise and other parameters. It is found that in all the three cases the fidelity tends to one as the noise parameter tends to zero.

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

Data Availability

Our manuscript has no associated data.

References

  1. Bennett, C.H., Brassard, G., Crepeau, 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, 1895–1899 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Kwek, L.-C., Cao, L., Luo, W., Wang, Y., Sun, S., Wang, X., Liu, A.Q.: Chip-based quantum key distribution. AAPPS Bull. 31, 15 (2021)

    Article  ADS  Google Scholar 

  3. Liu, B., Xia, S., Xiao, D., Huang, W., Xu, B., Li, Y.: Decoy-state method for quantum-key-distribution-based quantum private query. Science China. Physics, Mechanics and Astronomy. 65(4) 240312 (2022)

  4. Li, Z., Wei, K.: Improving parameter optimization in decoy-state quantum key distribution. Quantum Eng. 9717591 (2022). doi: 10.1155/2022/9717591

  5. Zhou, L., Sheng, Y-B.: One-step device-independent quantum secure direct communication. Science China. Physics, Mechanics and Astronomy. 65(5), 250311 (2022)

  6. Liu, X. et al.: Practical decoy-state quantum secure direct communication. Science China. Physics, Mechanics and Astronomy. 64(12), 120311 (2022)

  7. Shen, Y., Zhang, F.-L., Chen, Y.-Z., Zhou, C.-C.: Masking quantum information in the Kitaev Abelian anyons. Physica A. 612, 128495 (2023)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  9. Muralidharan, S., Panigrahi, P.K.: Perfect teleportation, quantum-state sharing and superdense coding through a genuinely entangled five-qubit state. Physical Review A. 77(3),032321(2008)

  10. Zhou, R.G., Li, X., Qian, C., et al.: Quantum Bidirectional Teleportation \(2\longleftrightarrow \) or \(2 \longleftrightarrow 3\) Qubit Teleportation Protocol Via 6-Qubit Entangled State. Int J Theor Phys. 59, 166–172 (2020). https://doi.org/10.1007/s10773-019-04306-1

    Article  MathSciNet  MATH  Google Scholar 

  11. Jiang, L.N.: Quantum Teleportation under Different Local Independent Noise Environment. Int J Theor Phys 58, 3899–3907 (2019). https://doi.org/10.1007/s10773-019-04256-8

    Article  MathSciNet  MATH  Google Scholar 

  12. Lo, H.K.: Classical-communication cost in distributed quantum-information processing. A generalization of quantum-communication complexity. Phys. Rev. A. 62, 012313 (2000)

  13. Wang, D., Liu, Y-m., Zhang, Z-j.: Remote preparation of a class of three-qubit states. Optics Communications 281, 871–875 (2008)

  14. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A. 63, 014302 (2001)

    Article  ADS  Google Scholar 

  15. Bennett, C.H., Divincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)

    Article  ADS  Google Scholar 

  16. Ye, M.Y., Zhang, Y.S., Guo, G.C.: Faithful remote state preparation using finite classical bits and a nonmaximally entangled state. Phys. Rev. A. 69, 022310 (2004)

    Article  ADS  Google Scholar 

  17. Xia, Y., Song, J., Song, H.S.: Multiparty remote state preparation. J. Phys. B-At. Mol. Opt. 40(18), 3719–3724 (2007)

    Article  ADS  Google Scholar 

  18. Wang, D.: Remote preparation of an arbitrary two-particle pure state via nonmaximally entangled states and positive operator-valued measurement. Int. J. Quantum Inf. 8(8), 1265–1275 (2010)

    Article  MATH  Google Scholar 

  19. Wang, D., Ye, L.: Optimizing scheme for remote preparation of four-particle cluster-like entangled states. Int. J. Theor. Phys. 50, 2748–2757 (2011)

    Article  MATH  Google Scholar 

  20. Wang, D., Hu, Y.-D., Wang, Z.-Q., Ye, L.: Efficient and faithful remote preparation of arbitrary three- and four-particle W-class entangled states. Quantum Inf. Process. 14(6), 2135–2151 (2015)

    Article  ADS  MATH  Google Scholar 

  21. Choudhury, B.S., Samanta, S.: Remote preparation of some three particle entangled states under divided information. Int J. Theor. Phys. 58, 83–91 (2019)

    Article  MATH  Google Scholar 

  22. Jia-yin, P., Hong-xuan, L.: Cyclic remote state preparation. Int. J. Theor. Phys. 60(4), 1593–1602 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chaudhary, M., Fadel, M., Ilo-Okeke, E.O., Pyrkov, A.N., Ivannikov, V., Byrnes, T.: Remote state preparation of two-component Bose-Einstein condensates. Phys. Rev. A. 103(6), 062417(2021)

  24. Lu, X.Q., Feng, K.H., Zhou, P.: Deterministic remote preparation of an arbitrary single-qudit state with high-dimensional spatial-mode entanglement via linear-optical elements. Int. J. Theor. Phys. 61, 36 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  25. Vaidman, L.: Teleportation of quantum states. Phys. Rev. A. 49(2), 1473–1476 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  26. Chen, X.-B., Sun, Y.-R., Xu, G., (...), Qu, Z., Yang, Y.-X.: Controlled bidirectional remote preparation of three-qubit state. Quantum Inf. Process. 16(10), 244 (2017)

  27. Dai, R., Li, HS. Asymmetric Bidirectional Quantum Teleportation via Seven-qubit Cluster State. Int J Theor Phys. 61, 187 (2022). DOIurlhttps://doi.org/10.1007/s10773-022-05157-z

  28. Zheng, Y., Li, D., Liu, X. et al. Quantum Teleportation of Unknown Seven-Qubit Entangled State Using Four-Qubit Entangled State. Int. J. Theor. Phys. 61, 138 (2022). DOIurl doi: 10.1007/s10773-022-05039-4

  29. Pandey, R.K., Yadav, P.S., Prakash, R. et al. Controlled Bidirectional Quantum Teleportation of Superposed Coherent State Using Five-mode Cluster-type Entangled Coherent State as a Resource. Int. J. Theor. Phys. 61, 104 (2022). DOIurlhttps://doi.org/10.1007/s10773-022-05080-3

  30. Kazemikhah, P., Aghababa, H.: Bidirectional Quantum Teleportation of an Arbitrary Number of Qubits by Using Four Qubit Cluster State. Int J Theor Phys 60, 378–386 (2021). https://doi.org/10.1007/s10773-020-04704-w

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhang, Z.J., Man, Z.X.: Many-agent controlled teleportation of multi-qubit quantum information. Phys. Lett. A. 341(1), 55–59 (2005)

    Article  ADS  MATH  Google Scholar 

  32. Gao, T., Yan, F.L., Wang, Z.X.: Controlled quantum teleportation and secure direct communication. Chin. Phys. B 14(5), 893–897 (2005)

    Article  Google Scholar 

  33. Zhang, Z.J.: Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message. Phys. Lett. A 352(1), 55–58 (2006)

    Article  ADS  MATH  Google Scholar 

  34. Liu, J.-C., Li, Y.-H., Nie, Y.-Y.: Controlled teleportation of an arbitrary two-particle pure or mixed state by using a five-qubit cluster state. Int. J. Theor. Phys. 49, 1976–1984 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  35. 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)

    Article  MathSciNet  Google Scholar 

  36. Zhang, D., Zha, X.W., Duan, Y.J.: Bidirectional and asymmetric quantum controlled teleportation. Int. J. Theor. Phys. 54, 1711–1719 (2015)

    Article  MATH  Google Scholar 

  37. Yang, Y.Q., Zha, X.W., Yu, Y.: Asymmetric bidirectional controlled teleportation via seven-qubit cluster state. Int. J. Theor. Phys. 55, 4197–4204 (2016)

    Article  MATH  Google Scholar 

  38. Hong, W.Q.: Asymmetric bidirectional controlled teleportation by using a seven-qubit entangled state. Int. J. Theor. Phys. 55(1), 384–387 (2016)

    Article  MATH  Google Scholar 

  39. Sang, Z.W.: Asymmetric bidirectional controlled remote state preparation by using a seven-particle entangled state. Int. J. Theor. Phys. 56, 3209–3212 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  40. Li, Y.-H., Qiao, Y., Sang, M.-H., Nie, Y.-Y.: Bidirectional controlled remote state preparation of an arbitrary two-qubit state. Int. J. Theor. Phys. 58(7), 2228–2234 (2019)

    Article  MATH  Google Scholar 

  41. Choudhury, B.S., Samanta, S.: A remote state preparation scheme initiated and fixed by a Mentor. Phys. P. Nucl. Lett. 16(6) (2019) 608–612

  42. Mandal, M.K., Choudhury, B.S., Samanta, S.: Cyclic controlled remote state preparation protocol initiated by a mentor for qubits. Opt Quant Electron 54, 602 (2022). DOIurlhttps://doi.org/10.1007/s11082-022-03959-3

  43. Yang, G., Lian, B.-W., Nie, M., Jin, J.: Bidirectional multi-qubit quantum teleportation in noisy channel aided with weak measurement. Chin. Phys. B 26(4), 040305 (2017)

    Article  ADS  Google Scholar 

  44. Zhou, P., Lv, L., He, L. M.: Effect of noise on remote preparation of an arbitrary single-qubit state. Quantum Eng. 3, e64 (2021). DOIurlhttps://doi.org/10.1002/que2.64

  45. Feng, K.H., Chen, Y.C., Zhou, P.: Protecting high-dimentional entanglement from decoherence via quantum weak measurement and reversal. Mod. Phys. Lett. A. 37(19), 2250117 (2022)

    Article  ADS  Google Scholar 

  46. 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 2n Bell states as quantum channel. Opt. and Quant. Electronics. 54(9), 568 (2022)

    Article  Google Scholar 

  47. Liang, Y. C., Yeh, Y. H., Mendonça, P. E. et al.: Quantum fidelity measures for mixed states. Rep. Prog. Phys. 82, 076001 (2019)

  48. Oh, S., Lee, S., Lee, H.W., et al.: Fidelity of quantum teleportation through noisy channels. Phy. Rev. A. 66, 022316 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  49. Fortes, R., Rigolin, G.: Fighting noise with noise in realistic quantum teleportation. Phys. Rev. A. 92, 012338 (2015)

    Article  ADS  Google Scholar 

  50. Yuan, H., et al.: Optimizing resource consumption, operation complexity and efficiency in quantum state sharing. J. Phys. B At. Mol. Opt. Phys. 41(14), 145506 (1–6) (2008)

  51. Choudhury, B.S., Samanta, S.: Perfect joint remote state preparation of arbitrary six-qubit cluster-type states. Quantum Inf. Process. 17, 175 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Ma, P.-C., Chen, G.-B., Li, X.-W., Zhang, J., Zhan, Y.-B.: Asymmetric controlled bidirectional remote state preparation by using a ten-qubit entangled state. Int. J. Theor. Phys. 56, 2716–2723 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  53. Sang, Z.-w.: Bidirectional controlled quantum information transmission by using a five-qubit cluster state. Int. J. Theor. Phys. 56:3400–3404 (2017)

Download references

Acknowledgements

This work is supported by the Indian Institute of Engineering Science and Technology, Shibpur. The valuable suggestions of the reviewer are gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Engineering Science and Technology, B. Garden, 711103, West Bengal, India

    Binayak S. Choudhury, Manoj Kumar Mandal & Soumen Samanta

Authors
  1. Binayak S. Choudhury
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manoj Kumar Mandal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Soumen Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors discussed the results and equally contributed to the final manuscript.

Corresponding author

Correspondence to Soumen Samanta.

Ethics declarations

Conflicts of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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

Choudhury, B.S., Mandal, M.K. & Samanta, S. Mentor Initiated Controlled Bi-directional Remote State Preparation Scheme For \((2 \iff 4)\)-Qubit Entangled States in Noisy Channel. Int J Theor Phys 62, 107 (2023). https://doi.org/10.1007/s10773-023-05336-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-023-05336-6

Keywords

Search

Navigation