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Entanglement purification of two-photon systems in multiple degrees of freedom

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Abstract

Hyperentanglement purification is a very important element for high-capacity long-distance quantum communication. We present an efficient hyperentanglement purification protocol (hyper-EPP) for nonlocal two-photon systems in three degrees of freedom (DoFs), including the polarization, the time-bin, and the spatial-mode DoFs. Our hyper-EPP is constructed with two steps resorting to polarization–time–spatial parity-check operation using the quantum nondemolition detector and SWAP gates, respectively. With this hyper-EPP, the bit-flip errors in the three DoFs can be corrected with high efficiency. The implementation of our hyper-EPP is contributed by a cross-Kerr nonlinearity between the signal photons and a coherent state via Kerr media, which could be achieved with current techniques. Moreover, some currently available optical elements are applied in the purification process, which offer facilities for the practical implementation. It is useful for long-distance high-capacity quantum communication with hyperentanglement in multiple DoFs.

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References

  1. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Yan, F.L., Gao, T., Chitambar, E.: Two local observables are sufficient to characterize maximally entangled states of N qubits. Phys. Rev. A 83, 022319 (2011)

    Article  ADS  Google Scholar 

  3. Gao, T., Yan, F.L., van Enk, S.J.: Permutationally invariant part of a density matrix and nonseparability of N-qubit states. Phys. Rev. Lett. 112, 180501 (2014)

    Article  ADS  Google Scholar 

  4. 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, 1895–1899 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. 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 

  6. Ekert, A.K.: Quantum cryptography based on Bell¡-s theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)

    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. Kwiat, P.G.: Hyper-entangled states. J. Mod. Opt. 44, 2173–2184 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Yang, T., Zhang, Q., Zhang, J., Yin, J., Zhao, Z., Zukowski, M.: All-versus-nothing violation of local realism by two-photon, four-dimensional entanglement. Phys. Rev. Lett. 95, 240406 (2005)

    Article  ADS  Google Scholar 

  12. Barreiro, J.T., Langford, N.K., Peters, N.A., Kwiat, P.G.: Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005)

    Article  ADS  Google Scholar 

  13. Vallone, G., Ceccarelli, R., De Martini, F., Mataloni, P.: Hyperentanglement of two photons in three degrees of freedom. Phys. Rev. A 79, 030301 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Ceccarelli, R., Vallone, G., De Martini, F., Mataloni, P., Cabello, A.: Experimental entanglement and nonlocality of a two-photon six-qubit cluster State. Phys. Rev. Lett. 103, 160401 (2009)

    Article  ADS  Google Scholar 

  15. Vallone, G., Donati, G., Ceccarelli, R., Mataloni, P.: Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation. Phys. Rev. A 81, 052301 (2010)

    Article  ADS  Google Scholar 

  16. Gao, W.B., Lu, C.Y., Yao, X.C., Xu, P., Guhne, O., Goebel, A., Chen, Y.A., Peng, C.Z., Chen, Z.B., Pan, J.W.: Experimental demonstration of a hyper-entangled ten-qubit Schröinger cat state. Nat. Phys. 6, 331–335 (2010)

    Article  Google Scholar 

  17. Kang, D.P., Helt, L.G., Zhukovsky, S.V., Torres, J.P., Sipe, J.E., Helmy, A.S.: Hyperentangled photon sources in semiconductor waveguides. Phys. Rev. A 89, 023833 (2014)

    Article  ADS  Google Scholar 

  18. Bhatti, D., von Zanthier, J., Agarwal, G.S.: Entanglement of polarization and orbital angular momentum. Phys. Rev. A 91, 062303 (2015)

    Article  ADS  Google Scholar 

  19. Kwiat, P.G., Weinfurter, H.: Embedded Bell-state analysis. Phys. Rev. A 58, 2623 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  20. Walborn, S.P., Pádua, S., Monken, C.H.: Hyperentanglement-assisted Bell-state analysis. Phys. Rev. A 68, 042313 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  21. Schuck, C., Huber, G., Kurtsiefer, C., Weinfurter, H.: Complete deterministic linear optics Bell state analysis. Phys. Rev. Lett. 96, 190501 (2006)

    Article  ADS  Google Scholar 

  22. Barbieri, M., Vallone, G., Mataloni, P., De Martini, F.: Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement. Phys. Rev. A 75, 042317 (2007)

    Article  ADS  Google Scholar 

  23. 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 

  24. Li, X.H., Ghose, S.: Self-assisted complete maximally hyperentangled state analysis via the cross-Kerr nonlinearity. Phys. Rev. A 93, 022302 (2016)

    Article  ADS  Google Scholar 

  25. Wang, T.J., Song, S.Y., Long, G.L.: Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities. Phys. Rev. A 85, 062311 (2012)

    Article  ADS  Google Scholar 

  26. Ren, B.C., Wei, H.R., Hua, M., Li, T., Deng, F.G.: Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities. Opt. Express 20, 24664–24677 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. 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 

  30. Walton, Z.D., Abouraddy, A.F., Sergienko, A.V., Saleh, B.E.A., Teich, M.C.: Decoherence-free subspaces in quantum key distribution. Phys. Rev. Lett. 91, 087901 (2003)

    Article  ADS  Google Scholar 

  31. Boileau, J.C., Gottesman, D., Laflamme, R., Poulin, D., Spekkens, R.W.: Robust polarization-based quantum key distribution over a collective-noise channel. Phys. Rev. Lett. 92, 017901 (2004)

    Article  ADS  Google Scholar 

  32. Boileau, J.C., Laflamme, R., Laforest, M., Myers, C.R.: Robust quantum communication using a polarization-entangled photon pair. Phys. Rev. Lett. 93, 220501 (2004)

    Article  ADS  Google Scholar 

  33. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)

    Article  ADS  Google Scholar 

  34. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A 77, 062325 (2008)

    Article  ADS  Google Scholar 

  35. Ren, B.C., Du, F.F., Deng, F.G.: Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys. Rev. A 88, 012302 (2013)

    Article  ADS  Google Scholar 

  36. Li, X.H., Ghose, S.: Hyperentanglement concentration for time-bin and polarization hyperentangled photons. Phys. Rev. A 91, 062302 (2015)

    Article  ADS  Google Scholar 

  37. Zhang, H., Wang, H.: Entanglement concentration of microwave photons based on the Kerr effect in circuit QED. Phys. Rev. A 95, 052314 (2017)

    Article  ADS  Google Scholar 

  38. Peng, Z.H., Zou, J., Liu, X.J., Xiao, Y.J., Kuang, L.M.: Atomic and photonic entanglement concentration via photonic Faraday rotation. Phys. Rev. A 86, 034305 (2012)

    Article  ADS  Google Scholar 

  39. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noise entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)

    Article  ADS  Google Scholar 

  40. Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S., Sanpera, A.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818–2821 (1996)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Pan, J.W., Gasparoni, S., Ursin, R., Weihs, G., Zeilinger, A.: Experimental entanglement purification of arbitrary unknown states. Nature 423, 417–422 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. Ren, B.C., Deng, F.G.: Hyperentanglement purification and concentration assisted by diamond NV centers inside photoic crystal cavities. Laser Phys. Lett. 10, 115201 (2013)

    Article  ADS  Google Scholar 

  46. 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 

  47. Wang, G.Y., Liu, Q., Deng, F.G.: Hyperentanglement purification for two-photon six-qubit quantum systems. Phys. Rev. A 94, 032319 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. 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 

  50. Nemoto, K., Munro, W.J.: Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004)

    Article  ADS  Google Scholar 

  51. Kalamidas, D.: Single-photon quantum error rejection and correction with linear optics. Phys. Lett. A 343, 331–335 (2005)

    Article  ADS  MATH  Google Scholar 

  52. Han, X., Hu, S., Guo, Q., Wang, H.F., Zhang, S.: Effective scheme for W-state fusion with weak cross-Kerr nonlinearities. Quantum Inf. Process. 14, 1919–1932 (2015)

    Article  ADS  MATH  Google Scholar 

  53. Dong, L., Wang, J.X., Li, Q.Y., Shen, H.Z., Dong, H.K., Xiu, X.M.: Nearly deterministic preparation of the perfect W state with weak cross-Kerr nonlinearities. Phys. Rev. A 93, 012308 (2016)

    Article  ADS  Google Scholar 

  54. Liu, A.P., Cheng, L.Y., Guo, Q., Zhang, S., Zhao, M.X.: Universal quantum gates for hybrid system assisted by atomic ensembles embedded in double-sided optical cavities. Sci. Rep. 7, 43675 (2017)

    Article  ADS  Google Scholar 

  55. Wang, M.Y., Yan, F.L., Gao, T.: Entanglement concentration for polarization-spatial-time-bin hyperentangled Bell states. Europhys Lett. 123, 60002 (2018)

    Article  ADS  Google Scholar 

  56. Soudagar, Y., Bussières, F., Berlín, G., Lacroix, S., Fernandez, J.M., Godbout, N.: Cluster-state quantum computing in optical fibers. J. Opt. Soc. Am. B 24, 226–230 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  57. Lin, Q., Li, J.: Quantum control gates with weak cross-Kerr nonlinearity. Phys. Rev. A 79, 022301 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  59. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)

    Article  ADS  Google Scholar 

  60. 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 

  61. Li, X.H., Ghose, S.: Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity. Opt. Express 23, 3550–3562 (2015)

    Article  ADS  Google Scholar 

  62. Zhang, H., Wang, H.B.: Entanglement concentration of microwave photons based on the Kerr effect in circuit QED. Phys. Rev. A 95, 052314 (2017)

    Article  ADS  Google Scholar 

  63. Li, X.H., Ghose, S.: Complete hyperentangled Bell state analysis for polarization and time-bin hyperentanglement. Opt. Express 24, 18388–18398 (2016)

    Article  ADS  Google Scholar 

  64. Liu, Q., Wang, G.Y., Zhang, M., Deng, F.G.: Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity. Sci. Rep. 6, 22016 (2016)

    Article  ADS  Google Scholar 

  65. Barrett, S.D., Kok, P., Nemoto, K., Beausoleil, R.G., Munro, W.J., Spiller, T.P.: Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities. Phys. Rev. A 71, 060302 (2005)

    Article  ADS  Google Scholar 

  66. Matsuda, N., Shimizu, R., Mitsumori, Y., Kosaka, H., Edamatsu, K.: Observation of optical-fibre Kerr nonlinearity at the single-photon level. Nat. Photonics 3, 95–98 (2009)

    Article  ADS  MATH  Google Scholar 

  67. Feizpour, A., Xing, X., Steinberg, A.M.: Amplifying single-photon nonlinearity using weak measurements. Phys. Rev. Lett. 107, 133603 (2011)

    Article  ADS  Google Scholar 

  68. Zhu, C., Huang, G.: Giant Kerr nonlinearity, controlled entangled photons and polarization phase gates in coupled quantum-well structures. Opt. Express 19, 23364–23376 (2011)

    Article  ADS  Google Scholar 

  69. Hoi, I.C., Kockum, A.F., Palomaki, T., Stace, T.M., Fan, B., Tornberg, L.: Giant cross-Kerr effect for propagating microwaves induced by an artificial atom. Phys. Rev. Lett. 111, 053601 (2013)

    Article  ADS  Google Scholar 

  70. Feizpour, A., Hallaji, M., Dmochowski, G., Steinberg, A.M.: Observation of the nonlinear phase shift due to single postselected photons. Nat. Phys. 11, 905–909 (2015)

    Article  Google Scholar 

  71. Wittmann, C., Andersen, U.L., Takeoka, M., Sych, D., Leuchs, G.: Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector. Phys. Rev. A 81, 062338 (2010)

    Article  ADS  Google Scholar 

  72. Gardiner, C.W., Zoller, P.: Quantum Noise. Springer, New York (2000)

    Book  MATH  Google Scholar 

  73. Louis, S.G.R., Munro, W.J., Spiller, T.P., Nemoto, K.: Loss in hybrid qubit-bus couplings and gates. Phys. Rev. A 78, 022326 (2008)

    Article  ADS  Google Scholar 

  74. Wang, X.W., Zhang, D.Y., Tang, S.Q., Xie, L.J., Wang, Z.Y., Kuang, L.M.: Photonic two-qubit parity gate with cross-Kerr nonlinearity. Phys. Rev. A 85, 052326 (2012)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11805050, 11475054, Hebei Natural Science Foundation of China under Grant Nos. A2019205190, A2018205125, and Graduate Scientific Innovative Foundation of the Education Department of Hebei Province under Grant No. CXZZBS2019079.

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  1. College of Physics, Hebei Normal University, Shijiazhuang, 050024, China

    Meiyu Wang & Fengli Yan

  2. School of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, China

    Ting Gao

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  1. Meiyu Wang
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Wang, M., Yan, F. & Gao, T. Entanglement purification of two-photon systems in multiple degrees of freedom. Quantum Inf Process 19, 206 (2020). https://doi.org/10.1007/s11128-020-02697-3

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