Skip to main content
SpringerLink
Log in

Controlled Bidirectional Quantum Teleportation of Superposed Coherent State Using Five-mode Cluster-type Entangled Coherent State as a Resource

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

Abstract

Recently, Aliloute et al. [Quantum Inf Process 20, 29 (2021)] proposed a scheme of bidirectional quantum teleportation of coherent state qubit using three-mode entangled coherent state as a resource with success probability 1/2. However, their scheme is not feasible due to some shortcomings. In this present work, we propose a scheme of bidirectional quantum teleportation of coherent state qubit between two distant partners Alice and Bob, with the consent of controller, Charlie. We use five-mode cluster-type entangled coherent state as the quantum resource to achieve this task. The scheme uses linear optical devices such as beam splitters, phase shifters, and photon counters. It is shown that for moderately large coherent amplitude, near perfect controlled bidirectional quantum teleportation can be obtained in terms of the average fidelity of teleportation.

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

Similar content being viewed by others

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(13), 1895 (1993)

    Article  MathSciNet  MATH  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Bouwmeester, D., Pan, J., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)

    Article  MATH  ADS  Google Scholar 

  4. Furusawa, A., Sørensen, J., Braunstein, S., Fuchs, C., Kimble, H., Polzik, E.: Unconditional quantum teleportation. Science 282, 706–709 (1998)

    Article  ADS  Google Scholar 

  5. Nielsen, M., Knill, E., Laflamme, R.: Complete quantum teleportation using nuclear magnetic resonance. Nature 396, 52–55 (1998)

    Article  ADS  Google Scholar 

  6. Zhang, T., Goh, K., Chou, C., Lodahl, P., Kimble, H.: Quantum teleportation of light beams. Phys. Rev. A 67, 033802 (2003)

    Article  ADS  Google Scholar 

  7. Riebe, M., Häffner, H., Roos, C., Hänsel, W., Benhelm, J., Lancaster, G., Körber, T., Becher, C., Schmidt-Kaler, F., James, D., et al.: Deterministic quantum teleportation with atoms. Nature 429, 734–737 (2004)

    Article  ADS  Google Scholar 

  8. Gao, W., Fallahi, P., Togan, E., Delteil, A., Chin, Y., Miguel-Sanchez, J., Imamoğlu, A.: Quantum teleportation from a propagating photon to a solid-state spin qubit. Nat. Commun. 4, 1–8 (2013)

    Article  Google Scholar 

  9. Pfaff, W., Hensen, B., Bernien, H., Dam, S., Blok, M., Taminiau, T., Tiggelman, M., Schouten, R., Markham, M., Twitchen, D., et al.: Unconditional quantum teleportation between distant solid-state quantum bits. Science 345, 532–535 (2014)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  10. Ren, J., Xu, P., Yong, H., Zhang, L., Liao, S., Yin, J., Liu, W., Cai, W., Yang, M., Li, L., et al.: Ground-to-satellite quantum teleportation. Nature 549, 70–73 (2017)

    Article  ADS  Google Scholar 

  11. Fiaschi, N., Hensen, B., Wallucks, A., Benevides, R., Li, J., Alegre, T., Gröblacher, S.: Optomechanical quantum teleportation. Nature Photonics 15, 817–821 (2021)

    Article  ADS  Google Scholar 

  12. Park, K., Lee, S., Jeong, H.: Quantum teleportation between particlelike and fieldlike qubits using hybrid entanglement under decoherence effects. Phys. Rev. A 86, 062301 (2012)

    Article  ADS  Google Scholar 

  13. Takeda, S., Mizuta, T., Fuwa, M., Van Loock, P., Furusawa, A.: Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature. 500, 315–318 (2013)

    Article  ADS  Google Scholar 

  14. Jeong, H., Bae, S., Choi, S.: Quantum teleportation between a single-rail single-photon qubit and a coherent-state qubit using hybrid entanglement under decoherence effects. Quantum Inform. Process. 15, 913–927 (2016)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  15. Podoshvedov, S.: Efficient quantum teleportation of unknown qubit based on DV-CV interaction mechanism. Entropy. 21, 150 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  16. Zukowski, M., Zeilinger, A., Horne, M., Ekert, A.: “Event-ready-detectors” Bell Experiment via entanglement swapping. Phys. Rev. Lett. 71 (1993)

  17. Briegel, H., Dür, W., Cirac, J., Zoller, P.: Quantum repeaters: The role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932 (1998)

    Article  ADS  Google Scholar 

  18. Roffe, J.: Quantum error correction: An introductory guide. Contemporary Phys. 60, 226–245 (2019)

    Article  ADS  Google Scholar 

  19. 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(6), 1740–1744 (2013)

    Article  MathSciNet  Google Scholar 

  20. Shukla, C., Banerjee, A., Pathak, A.: Bidirectional controlled teleportation by using 5-qubit states: A generalized view. Int. J. Theor. Phys. 52(10), 3790–3796 (2013)

    Article  Google Scholar 

  21. Li, Y.-h., Li, X.-l., Sang, M.-h., Nie, Y.-y., Wang, Z.-s.: Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state. Quantum Inform. Process. 12(12), 3835–3844 (2013)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  22. An, Y.: Bidirectional controlled teleportation via six-qubit cluster state. Int. J. Theor. Phys. 52(11), 3870–3873 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yan, C.: Bidirectional controlled quantum teleportation by using five-qubit entangled state. Int. J. Theor. Phys. 53(5), 1454–1458 (2014)

    Article  MATH  Google Scholar 

  24. Da, Z., Zha, X.-W., Duan, Y.-J.: Bidirectional and asymmetric quantum controlled teleportation. Int. J. Theor. Phys. 54(5), 1711–1719 (2015)

    Article  MATH  Google Scholar 

  25. Da, Z., Zha, X.W., Li, W., Yu, Y.: Bidirectional and asymmetric quantum controlled teleportation via maximally eight-qubit entangled state. Quantum Inf. Process. 14(10), 3835–3844 (2015)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  26. Ming-huang, S.: Bidirectional quantum controlled teleportation by using a seven-qubit entangled state. Int. J. Theor. Phys. 55(1), 380–383 (2016)

    Article  MATH  Google Scholar 

  27. Li, Y.-h., Jin, X.-m.: Bidirectional controlled teleportation by using nine-qubit entangled state in noisy environments. Quantum Inf. Process. 15(2), 929–945 (2016)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  28. Choudhury, B.S., Dhara, A.: A bidirectional teleportation protocol for arbitrary two-qubit state under the supervision of a third party. Int. J. Theor. Phys. 55(4), 2275–2285 (2016)

    Article  MATH  Google Scholar 

  29. Zhou, R.-G., Xu, R., Lan, H.: Bidirectional quantum teleportation by using six-qubit cluster state. IEEE Access 7, 44269–44275 (2019)

    Article  Google Scholar 

  30. Vikram, V.: Comment on “bidirectional quantum teleportation of two-qubit state via four-qubit cluster state”. Int. J. Theor. Phys. 59(11), 3329–3335 (2020)

    Article  MATH  Google Scholar 

  31. Verma, V.: Bidirectional quantum teleportation and cyclic quantum teleportation of multi-qubit entangled states via g-state. Int. J. Mod. Phys. B 34(28), 2050261 (2020)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  32. Vikram, V.: Bidirectional controlled quantum teleportation of multi-qubit entangled states via five-qubit entangled state. Physica Scripta (2020)

  33. Verma, V.: Bidirectional quantum teleportation and cyclic quantum teleportation of multi-qubit entangled states via g-state. Int. J. Mod. Phys. B 34(28), 2050261 (2020)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  34. Verma, V., Yadav, D., Mishra, D.: Improvement on cyclic controlled teleportation by using a seven-qubit entangled state. Optical And Quantum Electronics. 53, 1–11 (2021)

    Article  Google Scholar 

  35. 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), 1–11 (2021)

    Article  MathSciNet  Google Scholar 

  36. Verma, V.: Bidirectional controlled quantum teleportation of multi-qubit entangled states via five-qubit entangled state. Physica Scripta 96(3), 035105 (2021)

    Article  ADS  Google Scholar 

  37. Glauber, R.: Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766 (1963)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  38. Ralph, T., Gilchrist, A., Milburn, G., Munro, W., Glancy, S.: Quantum computation with optical coherent states. Phys. Rev. A. 68, 042319 (2003)

    Article  ADS  Google Scholar 

  39. Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)

    Article  ADS  Google Scholar 

  40. Arrazola, J., Lütkenhaus, N.: Quantum communication with coherent states and linear optics. Phys. Rev. A. 90, 042335 (2014)

    Article  MATH  ADS  Google Scholar 

  41. Joo, J., Munro, W., Spiller, T.: Quantum metrology with entangled coherent states. Phys. Rev. Lett. 107, 083601 (2011)

    Article  ADS  Google Scholar 

  42. Sanders, B.C.: Review of entangled coherent states. Journal of Physics A: Mathematical and Theoretical 45(24), 244002 (2012)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  43. van Enk, S.J., Hirota, O.: Entangled coherent states: Teleportation and decoherence. Phys. Rev. A 64(2), 022313 (2001)

    Article  ADS  Google Scholar 

  44. Prakash, H., Chandra, N., Prakash, R., et al.: Improving the teleportation of entangled coherent states. Phys. Rev. A 75(4), 044305 (2007)

    Article  ADS  Google Scholar 

  45. Prakash, H., Mishra, M.K.: Increase in average fidelity of quantum teleportation by decreasing entanglement. In: Proceedings of ICOP-2009, CSIO Chandigarh, India. Online available: http://csio. res. in, 8085

  46. Prakash, H., Chandra, N., Prakash, R., Shivani: Swapping between two pairs of nonorthogonal entangled coherent states. Int. J. Mod. Phys. B 23(08), 2083–2092 (2009)

    Article  MATH  ADS  Google Scholar 

  47. Prakash, H.: Quantum Teleportation. In: Emerging Trends in Electronic and Photonic Devices and Systems, 2009. ELECTRO’09. International Conference On, pp. 18–23. IEEE (2009)

  48. Prakash, H., Chandra, N., Prakash, R., Kumar, S.A.: Entanglement diversion between two pairs of entangled coherent states: Fidelity and decoherence. Int. J. Mod. Phys. B 23(04), 585–595 (2009)

    Article  MATH  ADS  Google Scholar 

  49. Prakash, H., Chandra, N., Prakash, R., Kumar, S.A.: Improving the entanglement diversion between two pairs of entangled coherent states. Int. J. Mod. Phys. B 24(17), 3331–3339 (2010)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  50. Prakash, H., Chandra, N., Prakash, R., Shivani: Almost perfect teleportation using 4-partite entangled states. Int. J. Mod. Phys. B 24(17), 3383–3394 (2010)

    Article  MATH  ADS  Google Scholar 

  51. Mishra, M.K., Prakash, H.: Teleportation of a two-mode entangled coherent state encoded with two-qubit information. Journal of Physics B: Atomic, Molecular and Optical Physics 43(18), 185501 (2010)

    Article  ADS  Google Scholar 

  52. Prakash, R., Pandey, R.K., Prakash, H.: Controlled entanglement diversion using ghz type entangled coherent state. Int. J. Theor. Phys. 58(4), 1227–1236 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  53. Pandey, R.K., Prakash, R., Prakash, H.: Controlled quantum teleportation of superposed coherent state using ghz entangled coherent state. Int. J. Theor. Phys. 58(10), 3342–3351 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  54. Pandey, R.K., Prakash, R., Prakash, H.: High success standard quantum teleportation using entangled coherent state and two-level atoms in cavities. Quantum Inf. Process. 20(10), 1–26 (2021)

    Article  MathSciNet  Google Scholar 

  55. Shukla, G., Mishra, K., Yadav, D., Pandey, R., Mishra, D.: Quantum-enhanced super-sensitivity of a Mach–Zehnder interferometer with superposition of schrödinger’s cat-like state and Fock state as inputs using a two-channel detection. JOSA B. 39, 59–68 (2022)

    Article  ADS  Google Scholar 

  56. Aliloute, S., El Allati, A., El Aouadi, I.: Bidirectional teleportation using coherent states. Quantum Inf. Process. 20(1), 1–16 (2021)

    Article  MathSciNet  Google Scholar 

  57. Dodonov, V.V., Malkin, I.A., Man’Ko, V.I.: Even and odd coherent states and excitations of a singular oscillator. Physica 72(3), 597–615 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  58. Prakash, H., Verma, V.: Minimum assured fidelity and minimum average fidelity in quantum teleportation of single qubit using non-maximally entangled states. Quantum Inf. Process. 11(6), 1951–1959 (2012)

    Article  MathSciNet  MATH  ADS  Google Scholar 

Download references

Acknowledgements

RKP dedicate this paper in the memory of Prof. Ranjana Prakash and Prof. Hari Prakash. May their soul rest in peace. RKP is thankful to UGC for providing financial assistance under CSIR-UGC SRF fellowship. Discussions with Dr. M K Mishra, Dr. O N Verma, Dr. V Verma and Ms. S Javed are gratefully acknowledged.

Funding

No funding was received.

Author information

Authors and Affiliations

  1. Physics Department, University of Allahabad, Prayagraj, 211002, India

    Ravi Kamal Pandey, Phool Singh Yadav, Ranjana Prakash & Hari Prakash

Authors
  1. Ravi Kamal Pandey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Phool Singh Yadav
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ranjana Prakash
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hari Prakash
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Authors contributed equally in completing the work.

Corresponding author

Correspondence to Ravi Kamal Pandey.

Ethics declarations

Consent for publication

All the authors have the consent for publication.

Conflict of Interests

Authors declare no conflict of interest.

Additional information

Publisher’s Note

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

Appendix

Appendix

Table 1 Various possible PC measurement results in modes 7, 8 with Alice, modes 9, 10 with Bob, and mode 5 with controller Charlie. For each case, the corresponding probability of occurrence, required unitary operation, teleported state and fidelity is given
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1007/s10773-022-05080-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10773-022-05080-3

Keywords

Search

Navigation