Skip to main content
Log in

Cyclic teleportation in noisy channel with nondemolition parity analysis and weak measurement

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We first put forward a scheme to teleport circularly arbitrary single-qubit states in a noise quantum channel. In our scheme, each sender preforms local nondemolition parity analysis based on cross-Kerr nonlinearities and publicizes the achieved outcome; the nearby receiver executes appropriate Pauli operation on his/her own qubit to obtain the original state. Due to the implementation of nondemolition parity analysis rather than Bell state measurement, the resource of Bell state can be achieved and applied to other potential tasks of quantum information processing. Further, we discuss the influence of quantum noise by the example of an amplitude damping channel and obtain the fidelity of the cyclic teleportation. Finally, we use the weak measurement and the corresponding reversing measurement to protect the quantum entanglement, which shows an effective enhancement of the cyclic 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
Fig. 4

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Chen, D., Zhao, S.-H., Shi, L., Liu, Y.: Measurement-device-independent quantum key distribution with pairs of vector vortex beams. Phys. Rev. A 93, 032320 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Liu, Z., Chen, H., Liu, W., Juan, X., Wang, D., Li, Zhiqiang: Quantum secure direct communication with optimal quantum superdense coding by using general four-qubit states. Quantum Inf. Process. 12(1), 587–599 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, William 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 

  5. Bouwmeester, D., Pan, J.-W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, Anton: Experimental quantum teleportation. Nature 390(6660), 575–579 (1997)

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Peng, J.-Y., Luo, M.-X., Mo, Z.-W.: Joint remote state preparation of arbitrary two-particle states via GHZ-type states. Quantum Inf. Process. 12(7), 2325–2342 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. 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(8), 1976–1984 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhang, Z.J.: Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message. Phys. Lett. A 352(1–2), 55–58 (2006)

    Article  ADS  MATH  Google Scholar 

  10. Man, Z.-X., Xia, Y.-J., An, N.B.: Genuine multiqubit entanglement and controlled teleportation. Phys. Rev. A 75, 052306 (2007)

    Article  ADS  Google Scholar 

  11. Zhu, F.-C., Jian-Zhong, D., Chen, X.-B., Wen, Q.-Y.: Probabilistic teleportation of multi-particle partially entangled state. Chin. Phys. B 17(3), 771–777 (2008)

    Article  ADS  Google Scholar 

  12. Yan, F.L., Yan, T.: Probabilistic teleportation via a non-maximally entangled ghz state. Chin. Sci. Bull. 55(10), 902–906 (2010)

    Article  Google Scholar 

  13. Hassanpour, S., Houshmand, M.: Bidirectional teleportation of a pure EPR state by using GHZ states. Quantum Inf. Process. 15(2), 905–912 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. 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 

  15. Peng, J.-Y., Bai, M.-Q., Mo, Z.-W.: Bidirectional quantum states sharing. Int. J. Theor. Phys. 55(5), 2481–2489 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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 

  17. Peng, J.-Y., Bai, M.-Q., Mo, Z.-W.: Deterministic multi-hop controlled teleportation of arbitrary single-qubit state. Int. J. Theor. Phys. 56(10), 3348–3358 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhan, H.-T., Xu-Tao, Y., Xiong, P.-Y., Zhang, Z.-C.: Multi-hop teleportation based on W state and EPR pairs. Chin. Phys. B 25(5), 050305 (2016)

    Article  Google Scholar 

  19. Chen, Y.-X., Jing, D., Liu, S.-Y., Wang, X.-H.: Cyclic quantum teleportation. Quantum Inf. Process. 16(8), 201 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Jin, X.-M., Ren, J.-G., Yang, B., Yi, Z.-H., Zhou, F., Xiao-Fan, X., Wang, S.-K., Yang, D., Yuan-Feng, H., Jiang, S., Yang, T., Yin, H., Chen, K., Peng, C.-Z., Pan, J.-W.: Experimental free-space quantum teleportation. Nat. Photonics 4(6), 376–381 (2010)

    Article  ADS  Google Scholar 

  21. Wang, X.-L., Cai, X.-D., Zu-En, S., Chen, M.-C., Dian, W., Li, L., Liu, N.-L., Chao-Yang, L., Pan, J.-W.: Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518(7540), 516–519 (2015)

    Article  ADS  Google Scholar 

  22. Sheng, Y.-B., Deng, F.-G., Long, G.L.: Complete hyperentangled-bell-state analysis for quantum communication. Phys. Rev. A 82, 032318 (2010)

    Article  ADS  Google Scholar 

  23. He, B., Ren, Y., Bergou, J.A.: Creation of high-quality long-distance entanglement with flexible resources. Phys. Rev. A 79, 052323 (2009)

    Article  ADS  Google Scholar 

  24. Peng, J.-Y., He, Y.: Annular controlled teleportation. Int. J. Theor. Phys. 58(10), 3271–3281 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  25. Li, Y.-H., Qiao, Y., Sang, M.-H., Nie, Y.-Y.: Controlled cyclic quantum teleportation of an arbitrary two-qubit entangled state by using a ten-qubit entangled state. Int. J. Theor. Phys. 58(5), 1541–1545 (2019)

    Article  MATH  Google Scholar 

  26. Jun, G., Hwang, T., Tsai, C.-W.: On the controlled cyclic quantum teleportation of an arbitrary two-qubit entangled state by using a ten-qubit entangled state. Int. J. Theor. Phys. 59(1), 200–205 (2020)

    Article  MATH  Google Scholar 

  27. Fan, W., Bai, M.-Q., Zhang, Y.-C., Liu, R.-J., Mo, Z.-W.: Cyclic quantum teleportation of an unknown multi-particle high-dimension state. Mod. Phys. Lett. B 34(05), 2050073 (2020)

    Article  MathSciNet  Google Scholar 

  28. Lin, Q., He, B.: Single-photon logic gates using minimal resources. Phys. Rev. A 80, 042310 (2009)

    Article  ADS  Google Scholar 

  29. Dong, L., Wang, J.-X., Li, Q.-Y., Dong, H.-K., Xiu, X.-M., Gao, Y.-J.: Teleportation of a general two-photon state employing a polarization-entangled \(\chi \)state with nondemolition parity analyses. Quantum Inf. Process. 15(7), 2955–2970 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)

    Article  ADS  Google Scholar 

  31. Terhal, B.M.: Quantum error correction for quantum memories. Rev. Mod. Phys. 87, 307–346 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  32. Dong, L., Wang, J.-X., Shen, H.-Z., Li, D., Xiu, X.-M., Gao, Y.-J., Yi, X.X.: Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel. Quantum Inf. Process. 13(6), 1413–1424 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Dong, L., Wang, J.-X., Li, Q.-Y., Shen, H.-Z., Dong, H.-K., Xiu, X.-M., Gao, Y.-J.: Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem. Opt. Lett. 41(5), 1030–1033 (2016)

    Article  ADS  Google Scholar 

  34. Pan, J.-W., Simon, C., Brukner, Č, Zeilinger, A.: Entanglement purification for quantum communication. Nature 410(6832), 1067–1070 (2001)

    Article  ADS  Google Scholar 

  35. Ren, B.-C., Fang-Fang, D., Deng, F.-G.: Two-step hyperentanglement purification with the quantum-state-joining method. Phys. Rev. A 90, 052309 (2014)

    Article  ADS  Google Scholar 

  36. Xu, G.F., Zhang, J., Tong, D.M., Sjöqvist, Erik, Kwek, L.C.: Nonadiabatic holonomic quantum computation in decoherence-free subspaces. Phys. Rev. Lett. 109, 170501 (2012)

    Article  ADS  Google Scholar 

  37. Li, C.-K., Nakahara, M., Poon, Y.-T., Sze, N.-S., Tomita, H.: Recursive encoding and decoding of the noiseless subsystem and decoherence-free subspace. Phys. Rev. A 84, 044301 (2011)

    Article  ADS  Google Scholar 

  38. Xiu, X.-M., Li, Q.-Y., Lin, Y.-F., Dong, H.-K., Dong, L., Gao, Y.-J.: Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-kerr nonlinearities. Phys. Rev. A 94, 042321 (2016)

    Article  ADS  Google Scholar 

  39. Xiu, X.-M., Li, Q.-Y., Dong, L., Shen, H.-Z., Li, D., Gao, Y.-J., Yi, X.X.: Distributing a multi-photon polarization-entangled state with unitary fidelity via arbitrary collective noise channels. Quantum Inf. Process. 14(1), 361–372 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Dong, L., Wang, J.-X., Li, Q.-Y., Shen, H.-Z., Dong, H.-K., Xiu, X.-M., Gao, Y.-J., Oh, C.H.: Nearly deterministic preparation of the perfect \(w\) state with weak cross-kerr nonlinearities. Phys. Rev. A 93, 012308 (2016)

    Article  ADS  Google Scholar 

  41. Dong, L., Lin, Y.-F., Li, Q.-Y., Xiu, X.-M., Dong, H.-K., Gao, Y.-J.: Optical proposals for controlled delayed-choice experiment based on weak cross-kerr nonlinearities. Quantum Inf. Process. 16(5), 122 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)

    Article  ADS  Google Scholar 

  43. Katz, N., Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., O’Connell, A., Wang, H., Cleland, A.N., Martinis, J.M., Korotkov, Alexander N.: Reversal of the weak measurement of a quantum state in a superconducting phase qubit. Phys. Rev. Lett. 101, 200401 (2008)

    Article  ADS  Google Scholar 

  44. Sun, Q., Al-Amri, M., Zubairy, M.S.: Reversing the weak measurement of an arbitrary field with finite photon number. Phys. Rev. A 80, 033838 (2009)

    Article  ADS  Google Scholar 

  45. Liao, X.-P., Fang, M.-F., Fang, J.-S., Zhu, Q.-Q.: Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement. Chin. Phys. B 23(2), 020304 (2014)

    Article  ADS  Google Scholar 

  46. Yang, G., Lian, B.-W., Nie, M.: Decoherence suppression for three-qubit W-like state using weak measurement and iteration method. Chin. Phys. B 25(8), 080310 (2016)

    Article  ADS  Google Scholar 

  47. Preskill, J.: Lecture notes for physics 229: quantum information and computation. California Institute of Technology, (1997)

  48. Kim, Y.-S., Cho, Y.-W., Ra, Y.-S., Kim, Y.-H.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17(14), 11978–11985 (2009)

    Article  ADS  Google Scholar 

  49. Kim, Y.-S., Lee, J.-C., Kwon, O., Kim, Y.-H.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8(2), 117–120 (2012)

    Article  Google Scholar 

  50. Lee, J.-C., Jeong, Y.-C., Kim, Y.-S., Kim, Y.-H.: Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19(17), 16309–16316 (2011)

    Article  ADS  Google Scholar 

  51. Uhlmann, A.: The transition probability in the state space of a \(*\)-algebra. Rep. Math. Phys. 9(2), 273–279 (1976)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41(12), 2315–2323 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is partial supported by the National Natural Science Foundation of China (Grant No. 11671284).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ming-Qiang Bai.

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

Peng, JY., Tang, L., Yang, Z. et al. Cyclic teleportation in noisy channel with nondemolition parity analysis and weak measurement. Quantum Inf Process 21, 114 (2022). https://doi.org/10.1007/s11128-022-03461-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-022-03461-5

Keywords

Navigation