Skip to main content
SpringerLink
Log in

Bidirectional and cyclic quantum dense coding in a high-dimension system

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In light of quantum dense coding in the case of high-dimension quantum states between two parties, by introducing additional local operations for encoding, we propose a brand-new bidirectional quantum dense coding scheme, in which two legitimate agents can simultaneously transmit their different encoded messages to each other. In addition, we present a bidirectional quantum dense coding scheme with a control by virtue of the generalized Hadamard transformation. We show how to implement the cyclic quantum dense coding in an arbitrary high dimension where Alice can transfer her encoded messages \(n_1m_1\) to Bob; meanwhile, Bob can transfer his encoded messages \(n_2m_2\) to Charlie and Charlie can also transfer his encoded messages \(n_3m_3\) to Alice in both clockwise and counterclockwise directions. We can also generalize the cyclic scheme to system having \(n\ge 3\) agents. Thereby, our scheme can realize dense coding in quantum information networks with n agents in arbitrary directions.

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

Similar content being viewed by others

References

  1. Bennett, C.H., Brassard, G., Crépeau, C., et al.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Gisin, N., Ribordy, G., Tittel, W., et al.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145 (2002)

    Article  ADS  MATH  Google Scholar 

  5. Mattle, K., Weinfurter, H., Kwiat, P.G., et al.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76(25), 4656 (1996)

    Article  ADS  Google Scholar 

  6. Liu, X.S., Long, G.L., Tong, D.M., et al.: General scheme for superdense coding between multiparties. Phys. Rev. A 65(2), 022304 (2002)

    Article  ADS  Google Scholar 

  7. Grudka, A., Wojcik, A.: Symmetric scheme for superdense coding between multiparties. Phys. Rev. A 66(1), 014301 (2002)

    Article  ADS  Google Scholar 

  8. Mozes, S., Oppenheim, J., Reznik, B.: Deterministic dense coding with partially entangled states. Phys. Rev. A 71(1), 012311 (2005)

    Article  ADS  Google Scholar 

  9. Pati, A.K., Parashar, P., Agrawal, P.: Probabilistic superdense coding. Phys. Rev. A 72(1), 012329 (2005)

    Article  ADS  Google Scholar 

  10. Bruß, D., Lewenstein, M., Sen, A., et al.: Dense coding with multipartite quantum states. Int. J. Quantum Inf. 4(3), 415–428 (2006)

    Article  MATH  Google Scholar 

  11. Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74(6), 062320 (2006)

    Article  ADS  Google Scholar 

  12. Li, L., Qiu, D.: The states of W-class as shared resources for perfect teleportation and superdense coding. J. Phys. A Math. Theor. 40(35), 10871 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Laurenza, R., Lupo, C., Lloyd, S., et al.: Dense coding capacity of a quantum channel. arXiv preprint arXiv:1903.09168 (2019)

  14. Hao, J.C., Li, C.F., Guo, G.C.: Controlled dense coding using the Greenberger–Horne–Zeilinger state. Phys. Rev. A 63(5), 054301 (2001)

    Article  ADS  Google Scholar 

  15. Situ, H.Z., Qiu, D.W.: Simultaneous dense coding. J. Phys. A Math. Theor. 43(5), 055301 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Huelga, S.F., Vaccaro, J.A., Chefles, A., et al.: Quantum remote control: teleportation of unitary operations. Phys. Rev. A 63(4), 042303 (2001)

    Article  ADS  MATH  Google Scholar 

  17. Fu, H.Z., Tian, X.L., Hu, Y.: A general method of selecting quantum channel for bidirectional quantum teleportation. Int. J. Theor. Phys. 53(6), 1840–1847 (2014)

    Article  MATH  Google Scholar 

  18. Zha, X.W., Zou, Z.C., Qi, J.X., et al.: Bidirectional quantum controlled teleportation via five-qubit cluster state. Int. J. Theor. Phys. 52(6), 1740–1744 (2013)

    Article  MathSciNet  Google Scholar 

  19. Zhang, Z.J., Man, Z.X.: Secure direct bidirectional communication protocol using the Einstein–Podolsky–Rosen pair block. arXiv preprint arXiv:quant-ph/0403215 (2004)

  20. Sarvaghad-Moghaddam, M.: Efficient controlled bidirectional quantum secure direct communication using entanglement swapping and EPR pairs. arXiv preprint arXiv:1902.11188 (2019)

  21. Peng, J.Y., Bai, M.Q., Mo, Z.W.: Bidirectional controlled joint remote state preparation. Quantum Inf. Process. 14(11), 4263–4278 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Wang, X.Y., Mo, Z.W.: Bidirectional controlled joint remote state preparation via a seven-qubit entangled state. Int. J. Theor. Phys. 56(4), 1052–1058 (2017)

    Article  MATH  Google Scholar 

  23. Chen, Y.X., Du, J., Liu, S.Y., et al.: Cyclic quantum teleportation. Quantum Inf. Process. 16(8), 201 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Vaziri, A., Weihs, G., Zeilinger, A.: Experimental two-photon, three-dimensional entanglement for quantum communication. Phys. Rev. Lett. 89(24), 240401 (2002)

    Article  ADS  Google Scholar 

  25. Dada, A.C., Leach, J., Buller, G.S., et al.: Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities. Nat. Phys. 7(9), 677 (2011)

    Article  Google Scholar 

  26. Agnew, M., Leach, J., McLaren, M., et al.: Tomography of the quantum state of photons entangled in high dimensions. Phys. Rev. A 84(6), 062101 (2011)

    Article  ADS  Google Scholar 

  27. Giovannini, D., Romero, J., Leach, J., et al.: Characterization of high-dimensional entangled systems via mutually unbiased measurements. Phys. Rev. Lett. 110(14), 143601 (2013)

    Article  ADS  Google Scholar 

  28. Krenn, M., Huber, M., Fickler, R., et al.: Generation and confirmation of a (100\(\times \)100)-dimensional entangled quantum system. Proc. Natl. Acad. Sci. 111(17), 6243–6247 (2014)

    Article  ADS  Google Scholar 

  29. Malik, M., Erhard, M., Huber, M., et al.: Multi-photon entanglement in high dimensions. Nat. Photon. 10(4), 248 (2016)

    Article  ADS  Google Scholar 

  30. Zhang, Y., Roux, F.S., Konrad, T., et al.: Engineering two-photon high-dimensional states through quantum interference. Sci. Adv. 2(2), e1501165 (2016)

    Article  ADS  Google Scholar 

  31. Fujiwara, M., Takeoka, M., Mizuno, J., et al.: Exceeding the classical capacity limit in a quantum optical channel. Phys. Rev. Lett. 90(16), 167906 (2003)

    Article  ADS  Google Scholar 

  32. Mafu, M., Dudley, A., Goyal, S., et al.: Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases. Phys. Rev. A 88(3), 032305 (2013)

    Article  ADS  Google Scholar 

  33. Cerf, N.J., Bourennane, M., Karlsson, A., et al.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88(12), 127902 (2002)

    Article  ADS  Google Scholar 

  34. Durt, T., Kaszlikowski, D., Chen, J.L., et al.: Security of quantum key distributions with entangled qudits. Phys. Rev. A 69(3), 032313 (2004)

    Article  ADS  Google Scholar 

  35. Huber, M., Pawlowski, M.: Weak randomness in device-independent quantum key distribution and the advantage of using high-dimensional entanglement. Phys. Rev. A 88(3), 032309 (2013)

    Article  ADS  Google Scholar 

  36. Kaszlikowski, D., Gnaciski, P., Żukowski, M., et al.: Violations of local realism by two entangled N-dimensional systems are stronger than for two qubits. Phys. Rev. Lett. 85(21), 4418 (2000)

    Article  ADS  Google Scholar 

  37. Son, W., Lee, J., Kim, M.S.: Generic Bell inequalities for multipartite arbitrary dimensional systems. Phys. Rev. Lett. 96(6), 060406 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  38. Collins, D., Gisin, N., Linden, N., et al.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88(4), 040404 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Cerf, N.J., Massar, S., Pironio, S.: Greenberger–Horne–Zeilinger paradoxes for many qudits. Phys. Rev. Lett. 89(8), 080402 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Lanyon, B.P., Barbieri, M., Almeida, M.P., et al.: Simplifying quantum logic using higher-dimensional Hilbert spaces. Nat. Phys. 5(2), 134 (2009)

    Article  Google Scholar 

  41. Mair, A., Vaziri, A., Weihs, G., et al.: Entanglement of the orbital angular momentum states of photons. Nature 412(6844), 313 (2001)

    Article  ADS  Google Scholar 

  42. Gu, B., Li, C.Q., Xu, F., et al.: High-capacity three-party quantum secret sharing with superdense coding. Chin. Phys. B 18(11), 4690 (2009)

    Article  ADS  Google Scholar 

  43. Stenholm, S., Bardroff, P.J.: Teleportation of N-dimensional states. Phys. Rev. A 58(6), 4373 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  44. Zhan, Y.B.: Controlled teleportation of high-dimension quantum-states with generalized Bell-state measurement. Chin. Phys. 16(9), 2557 (2007)

    Article  ADS  Google Scholar 

  45. Wang, C., Deng, F.G., Li, Y.S., et al.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71(4), 044305 (2005)

    Article  ADS  Google Scholar 

  46. Karimipour, V., Bahraminasab, A., Bagherinezhad, S.: Quantum key distribution for d-level systems with generalized Bell states. Phys. Rev. A 65(5), 052331 (2002)

    Article  ADS  Google Scholar 

  47. Gottesman, D.: Fault-tolerant quantum computation with higher-dimensional systems. Physics 10(10), 302–313 (1998)

    MathSciNet  MATH  Google Scholar 

  48. Wang, F., Erhard, M., Babazadeh, A., et al.: Generation of the complete four-dimensional Bell basis. Optica 4(12), 1462–1467 (2017)

    Article  ADS  Google Scholar 

  49. Reck, M., Zeilinger, A., Bernstein, H.J., et al.: Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73(1), 58 (1994)

    Article  ADS  Google Scholar 

  50. Lanyon, B.P., Weinhold, T.J., Langford, N.K., et al.: Manipulating biphotonic qutrits. Phys. Rev. Lett. 100(6), 060504 (2008)

    Article  ADS  Google Scholar 

  51. Lin, Q., He, B.: Bi-directional mapping between polarization and spatially encoded photonic qutrits. Phys. Rev. A 80(6), 062312 (2009)

    Article  ADS  Google Scholar 

  52. Lin, Q.: Optical realization of universal unitary operation of single partite polarization encoded qudit. Sci. Sin. 44(3), 317–325 (2014)

    Google Scholar 

  53. Babazadeh, A., Erhard, M., Wang, F., et al.: High-dimensional single-photon quantum gates: concepts and experiments. Phys. Rev. Lett. 119(18), 180510 (2017)

    Article  ADS  Google Scholar 

  54. Calsamiglia, J.: Generalized measurements by linear elements. Phys. Rev. A 65(3), 030301 (2002)

    Article  ADS  Google Scholar 

  55. Zhang, H., Zhang, C., Hu, X.M., et al.: Arbitrary two-particle high-dimensional Bell-state measurement by auxiliary entanglement. Phys. Rev. A 99(5), 052301 (2019)

    Article  ADS  Google Scholar 

  56. Hu, X.M., Guo, Y., Liu, B.H., et al.: Beating the channel capacity limit for superdense coding with entangled ququarts. Sci. Adv. 4(7), eaat9304 (2018)

    Article  ADS  Google Scholar 

  57. Guo, Y., Liu, B.H., Li, C.F., et al.: Advances in quantum dense coding. Adv. Quantum Technol. 2(5–6), 1900011 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank all of the editors and reviewers for their valuable suggestions, which have substantially improved this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 11671284), Sichuan Province Science and Technology Support Program (Grant No. 2017JY0197). The Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (Grant No. 2018QYJ02).

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 611756, China

    Xue Yang

  2. School of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China

    Xue Yang, Ming-qiang Bai, Zhi-wen Mo & Yi Xiang

  3. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu, 610066, China

    Xue Yang, Ming-qiang Bai, Zhi-wen Mo & Yi Xiang

  4. School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, China

    Yi Xiang

Authors
  1. Xue Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ming-qiang Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi-wen Mo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yi Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xue Yang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Bai, Mq., Mo, Zw. et al. Bidirectional and cyclic quantum dense coding in a high-dimension system. Quantum Inf Process 19, 43 (2020). https://doi.org/10.1007/s11128-019-2526-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-019-2526-9

Keywords

Search

Navigation