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Economical multi-photon polarization entanglement purification with Bell state

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Abstract

We present an economical entanglement purification protocol for the multi-photon polarization-entangled system in a Greenberger–Horne–Zeilinger (GHZ) state. We use one pair of two-photon Bell state or M-photon GHZ state (\(M<N\)) to correct the error in the polarization entanglement of an N-photon system. This protocol only uses linear optical elements, so that it is feasible in current experiment. The parties can obtain a high-quality entangled polarization state from each less-entangled N-photon system, by consuming only the Bell state, or the M-photon GHZ state. It is far different from conventional multipartite entanglement purification protocols. It also requires less local operation and classical communication than other purification protocols. Our protocol especially suits for the case where we can precisely know which channel or channels are more noisy. This protocol may be useful in current and future long-distance quantum communication.

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References

  1. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge Univ. Press, Cambridge (2000)

    MATH  Google Scholar 

  2. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  MATH  Google Scholar 

  3. 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 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Hu, X.M., Zhang, C., Zhang, C.J., Liu, B.H., Huang, Y.F., Han, Y.J., Li, C.F., Guo, G.C.: Experimental certification for nonclassical teleportation. Quan. Engineer. 1, e3 (2019)

    Google Scholar 

  5. Yan, Z.H., Qin, J.L., Qin, Z.Z., Su, X.L., Jia, X.J., Xie, C.D., Peng, K.C.: Generation of non-classical states of light and their application in deterministic quantum teleportation. Funda. Res. 1, 43–49 (2021)

    Article  Google Scholar 

  6. Ekert, A.K.: Quantum crytography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)

  7. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  9. Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)

    Article  ADS  Google Scholar 

  10. Zhang, W., Ding, D.S., Sheng, Y.B., Zhou, L., Shi, B.S., Guo, G.C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118, 220501 (2017)

    Article  ADS  Google Scholar 

  11. He, Y.F., Ma, W.P.: Multiparty quantum secure direct communication immune to collective noise. Quan. Inf. Process. 18, 4 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Zhou, L., Sheng, Y.B., Long, G.L.: Device-independent quantum secure direct communication against collective attacks. Sci. Bull. 65, 12–20 (2020)

    Article  Google Scholar 

  13. Liu, L., Niu, J.L., Fan, C.R., et al.: High-dimensional measurement-device-independent quantum secure direct communication. Quan. Inf. Process. 19, 404 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  14. Wu, J.W., Lin, Z.S., Yin, L.G., Long, G.L.: Security of quantum secure direct communication based on Wyner’s wiretap channel theory. Quan. Engineer. 1, e26 (2019)

  15. Li, T., Long, G.L.: Quantum secure direct communication based on single-photon Bell-state measurement. New J. Phys. 22, 063017 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  16. Zou, Z.K., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent quantum secure direct communication of multiple degrees of freedom of a single photon. EPL 131, 40005 (2020)

    Article  ADS  Google Scholar 

  17. Li, T., Gao, Z.K., Li, Z.H.: Measurement-device-independent quantum secure direct communication: Direct quantum communication with imperfect measurement device and untrusted operator. EPL 131, 60001 (2020)

    Article  ADS  Google Scholar 

  18. Wang, C.: Quantum secure direct communication: Intersection of communication and cryptography. Funda. Res. 1, 91 (2021)

    Article  Google Scholar 

  19. Zhou, N.R., Zhu, K.N., Zou, X.F.: Multi-party semi-quantum key distribution protocol with four-particle cluster states. Ann. Phys-Berlin 531, 1800520 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  20. Zhou, N.R., Huang, L.X., Gong, L.H., Zeng, Q.W.: Novel quantum image compression and encryption algorithm based on DQWT and 3D hyper-chaotic Henon map. Quan. Inf. Process. 19, 284 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zhou, N.R., Xu, Q.D., Du, N.S., Gong, L.H.: Semi-quantum private comparison protocol of size relation with d-dimensional Bell states. Quan. Inf. Process. 20, 124 (2021)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  23. Deng, F.G., Li, C.Y., Li, Y.S., Zhou, H.Y., Wang, Y.: Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement. Phys. Rev. A 72, 022338 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)

    Article  ADS  Google Scholar 

  26. Song, Y., Li, Z., Li, Y.: A dynamic multiparty quantum direct secret sharing based on generalized GHZ states. Quan. Inf. Process. 17, 244 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Zhang, K.J., Zhang, X., Jia, H.Y., et al.: A new n-party quantum secret sharing model based on multiparty entangled states. Quan. Inf. Process. 18, 81 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)

    Article  ADS  Google Scholar 

  29. Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)

    Article  ADS  Google Scholar 

  30. Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs. Phys. Rev. A 72, 044301 (2005)

    Article  ADS  Google Scholar 

  31. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1996)

    Article  ADS  Google Scholar 

  32. Deutsch, D., Ekert, A., Jozsa, R., et al.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818 (1996)

    Article  ADS  Google Scholar 

  33. Murao, M., Plenio, M.B., Popescu, S., Vedral, V., Knight, P.L.: Multiparticle entanglement purification protocols. Phys. Rev. A 57, R4075 (1998)

    Article  ADS  Google Scholar 

  34. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Multipartite entanglement purification with quantum nondemolition detectors. Eur. Phys. J. D 55, 235–242 (2009)

    Article  ADS  Google Scholar 

  35. Sheng, Y.B., Deng, F.G., Long, G.L.: Efficient polarization entanglement concentration for electrons with charge detection. Phys. Lett. A 375, 396 (2011)

    Article  ADS  Google Scholar 

  36. Horodecki, M., Horodecki, P.: Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A 59, 4206 (1999)

    Article  ADS  Google Scholar 

  37. Cheong, Y.W., Lee, S.W., Lee, J., Lee, H.W.: Entanglement purification for high-dimensional multipartite systems. Phys. Rev. A 76, 042314 (2007)

    Article  ADS  Google Scholar 

  38. Huber, M., Plesch, M.: Purification of genuine multipartite entanglement. Phys. Rev. A 83, 062321 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Pan, J.W., Gasparonl, S., Ursin, R., Weihs, G., Zellinger, A.: Experimental entanglement purification of arbitrary unknown states. Nature (London) 423, 417 (2003)

    Article  ADS  Google Scholar 

  41. Simon, C., Pan, J.W.: Polariztion entanglement purification using spatial entanglement. Phys. Rev. Lett. 89, 257901 (2002)

    Article  ADS  Google Scholar 

  42. Dür, W., Briegel, H.J.: Entanglement purification and quantum error correction. Rep. Prog. Phys. 70, 1381 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  43. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A 77, 042308 (2008)

    Article  ADS  Google Scholar 

  44. Xiao, L., Wang, C., Zhang, W., Huang, Y.D., Peng, J.D., Long, G.L.: Efficient strategy for sharing entanglement via noisy channels with doubly entangled photon pairs. Phys. Rev. A 77, 042315 (2008)

    Article  ADS  Google Scholar 

  45. Wang, C., Sheng, Y.B., Li, X.H., Deng, F.G., Zhang, W., Long, G.L.: Efficient entanglement purification for doubly entangled photon state. Sci. China Ser. E: Tech. Sci. 52, 3464–3467 (2009)

    Article  ADS  MATH  Google Scholar 

  46. Wang, C., Zhang, Y., Jin, G.S.: Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A 84, 032307 (2011)

    Article  ADS  Google Scholar 

  47. Sheng, Y.B., Deng, F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)

    Article  ADS  Google Scholar 

  48. Sheng, Y.B., Deng, F.G.: One-step deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044305 (2010)

    Article  ADS  Google Scholar 

  49. Li, X.H.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044304 (2010)

    Article  ADS  Google Scholar 

  50. Deng, F.G.: One-step error correction for multipartite polarization entanglement. Phys. Rev. A 83, 062316 (2011)

    Article  ADS  Google Scholar 

  51. Deng, F.G.: Efficient multipartite entanglement purification with the entanglement link from a subspace. Phys. Rev. A 84, 052312 (2011)

    Article  ADS  Google Scholar 

  52. Sheng, Y.B., Deng, F.G., Long, G.L.: One-step deterministic multipartite entanglement purification with linear optics. Phys. Lett. A 376, 314–319 (2012)

    Article  ADS  MATH  Google Scholar 

  53. Sangouard, N., Simon, C., Coudreau, T., Gisin, N.: Purification of single-photon entanglement with linear optics. Phys. Rev. A 78, 050301(R) (2009)

    Article  Google Scholar 

  54. Sheng, Y.B., Zhou, L., Long, G.L.: Hybrid entanglement purification for quantum repeaters. Phys. Rev. A 88, 022302 (2013)

    Article  ADS  Google Scholar 

  55. Zwerger, M., Briegel, H.J., Dür, W.: Universal and optimal error thresholds for measurement-based entanglement purification. Phys. Rev. Lett. 110, 260503 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  57. Zwerger, M., Briegel, H.J., Dür, W.: Robust of hashing protocols for entanglement purification. Phys. Rev. A 90, 012314 (2014)

    Article  ADS  Google Scholar 

  58. Wang, G.Y., Li, T., Ai, Q., Alsaedi, A., Hayat, T., Deng, F.G.: Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems. Phys. Rev. Appl. 10, 054058 (2018)

    Article  ADS  Google Scholar 

  59. Zhou, L., Sheng, Y.B.: Purification of logic-qubit entanglement. Sci. Rep. 6, 28813 (2016)

    Google Scholar 

  60. Chen, L.K., Yong, H.L., Xu, P., Yao, X.C., Xiang, T., et al.: Experimental nested purification for a linear optical quantum repeater. Nat. Photon. 11, 695 (2017)

    Article  ADS  Google Scholar 

  61. Zhou, L., Sheng, Y.B.: Polarization entanglement purification for concatenated Greenberger-Horne-Zeilinger state. Ann. Phys. 385, 10–35 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. Zhang, H., Liu, Q., Xu, X.S., Xiong, J., Alsaedi, A., Hayat, T., Deng, F.G.: Polarization entanglement purification of nonlocal microwave photons based on the cross-Kerr effect in circuit QED. Phys. Rev. A 96, 052330 (2017)

    Article  ADS  Google Scholar 

  63. Miguel-Ramiro, J., Dür, W.: Efficient entanglement purification protocols for d-level systems. Phys. Rev. A 98, 042309 (2018)

    Article  ADS  Google Scholar 

  64. Wu, X.D., Zhou, L., Zhong, W., Sheng, Y.B.: Purification of the concatenated Greenberger-Horne-Zeilinger state with linear optics. Quan. Inform. Process. 17, 255 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  65. Behera, B.K., Seth, S., Das, A., Panigrahi, P.K.: Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer. Quan. Inform. Process. 18, 108 (2019)

    Article  ADS  MATH  Google Scholar 

  66. Wang, R., Wang, T.J., Wang, C.: Entanglement purification and concentration based on hybrid spin entangled states of separate nitrogen-vacancy centers. EPL 126, 40006 (2019)

    Article  ADS  Google Scholar 

  67. Krastanov, S., Albert, V.V., Jiang, L.: Optimized entanglement purification. Quantum 3, 123 (2019)

    Article  Google Scholar 

  68. Zhou, L., Sheng, Y.B.: Purification of the residual entanglement. Opt. Express 28, 2291 (2020)

    Article  ADS  Google Scholar 

  69. Zhou, L., Zhang, S.S., Zhong, W., Sheng, Y.B.: Multi-copy nested entanglement purification for quantum repeaters. Ann. Phys. 412, 16842 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  70. Wang, G.Y., Long, G.L.: Entanglement purification for memory nodes in a quantum network. Sci. China-Phys. Mech. Astron. 63, 220311 (2020)

    Article  ADS  Google Scholar 

  71. Riera-Sàbat, F., Sekatski, P., Pirker, A., Dur, W.: Entanglement-assisted entanglement purification. Phys. Rev. Lett. 127, 040502 (2021)

  72. Riera-Sàbat, F., Sekatski, P., Pirker, A., Dur, W.: Entanglement purification by counting and locating errors with entangling measurements. Phys. Rev. A 104, 012419 (2021)

  73. Wang, M.Y., Yan, F.L., Gao, T.: Entanglement purification of two-photon systems in multiple degrees of freedom. Quan. Inform. Process. 19, 206 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  74. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Feasible time-bin entanglement purification based on sum-frequency generation. Opt. Express 29, 571 (2021)

    Article  ADS  Google Scholar 

  75. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Feasible measurement-based entanglement purification in linear optics. Opt. Express 29, 9363 (2021)

    Article  ADS  Google Scholar 

  76. Hu, X.M., Huang, C.X., Sheng, Y.B., Zhou, L., Liu, B.H., Guo, Y., Zhang, C., Xing, W.B., Huang, Y.F., Li, C.F., Guo, G.C.: Long-distance entanglement purification for quantum communication. Phys. Rev. Lett. 126, 010503 (2021)

    Article  ADS  Google Scholar 

  77. Zhou, L., Sheng, Y.B.: High-efficient two-step entanglement purification using hyperentanglement. arXiv: 2101.09006 (2021)

  78. Kok, P., Munro, W.J., Nemoto, K., Ralph, T.C., Dowing, J.P., Milburn, G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135 (2007)

    Article  ADS  Google Scholar 

  79. Shapiro, J.H.: Single-photon Kerr nonlinearities do not help quantum computation. Phys. Rev. A 73, 062305 (2006)

    Article  ADS  Google Scholar 

  80. Lu, C.Y., Zhou, X.Q., Gühne, O., Gao, W.B., Zhang, J., Yuan, Z.S., Goebel, A., Yang, T., Pan, J.W.: Experimental entanglement of six photons in graph states. Nat. Phys. 3, 91 (2007)

    Article  Google Scholar 

  81. Zhong, H.S., Li, Y., Li, W., et al.: 12-Photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion. Phys. Rev. Lett. 121, 250505 (2018)

    Article  ADS  Google Scholar 

  82. Zhao, B., Chen, Z.B., Chen, Y.A., Schmiedmayer, J., Pan, J.W.: Robust creation of entanglement between remote memory qubits. Phys. Rev. Lett. 98, 240502 (2007)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11974189).

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Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Lan Zhou

  2. College of Telecommunications & Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Ze-Kai Liu, Yi-Lun Cui, Hai-Jiang Ran & Yu-Bo Sheng

  3. Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Yu-Bo Sheng

  4. Bell Honors School, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Zi-Xuan Xu

  5. Key Lab of Broadband Wireless Communication and Sensor Network Technology, Ministry of Education, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Lan Zhou & Yu-Bo Sheng

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  1. Lan Zhou
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  2. Ze-Kai Liu
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Zhou, L., Liu, ZK., Xu, ZX. et al. Economical multi-photon polarization entanglement purification with Bell state. Quantum Inf Process 20, 257 (2021). https://doi.org/10.1007/s11128-021-03192-z

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