Abstract
We present a self-error-correction spatial-polarization hyperentanglement distribution scheme for N-photon systems in a hyperentangled Greenberger–Horne–Zeilinger state over arbitrary collective-noise channels. In our scheme, the errors of spatial entanglement can be first averted by encoding the spatial-polarization hyperentanglement into the time-bin entanglement with identical polarization and defined spatial modes before it is transmitted over the fiber channels. After transmission over the noisy channels, the polarization errors introduced by the depolarizing noise can be corrected resorting to the time-bin entanglement. Finally, the parties in quantum communication can in principle share maximally hyperentangled states with a success probability of 100%.


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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, 1895–1899 (1993)
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)
Liu, X.S., Long, G.L., Tong, D.M., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65, 022304 (2002)
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India. IEEE, New York (1984)
Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)
Pinheiro, P.V.P., Ramos, R.V.: Two-layer quantum key distribution. Quantum Inf. Process. 14, 2111–2124 (2015)
Hillery, M., Buz̆ek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)
Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)
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)
Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)
Hu, J.Y., Yu, B., Jing, M.Y., Xiao, L.T., Jia, S.T., Qin, G.Q., Long, G.L.: Experimental quantum secure direct communication with single photons. Light: Sci. Appl. 5, e16144 (2016)
Wang, C., Deng, F.G., Li, Y.S., Liu, X.S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)
Li, X.H.: Quantum secure direct communication. Acta Phys. Sin. 64, 160307 (2015)
Karlsson, A., Bourennane, M.: Quantum teleportation using three-particle entanglement. Phys. Rev. A 58, 4394 (1998)
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)
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)
Boileau, J.C., Laflamme, R., Laforest, M., Myers, C.R.: Robust quantum communication using a polarization-entangled photon pairs. Phys. Rev. Lett. 93, 220501 (2004)
Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)
Kalamidas, D.: Single-photon quantum error rejection and correction with linear optics. Phys. Lett. A 343, 331–335 (2005)
Li, X.H., Deng, F.G., Zhou, H.Y.: Faithful qubit transmission against collective noise without ancillary qubits. Appl. Phys. Lett. 91, 144101 (2007)
Yamamoto, T., Shimamura, J., Ödemir, S.K., Koashi, M., Imoto, N.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95, 040503 (2005)
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, 722–725 (1996)
Sheng, Y.B., Deng, F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)
Sheng, Y.B., Deng, F.G.: One-step deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044305 (2010)
Li, X.H.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044304 (2010)
Deng, F.G.: One-step error correction for multipartite polarization entanglement. Phys. Rev. A 83, 062316 (2011)
Sheng, Y.B., Zhou, L.: Deterministic polarization entanglement purification using time-bin entanglement. Laser Phys. Lett. 11, 085203 (2014)
Sheng, Y.B., Zhou, L.: Deterministic entanglement distillation for secure double-server blind quantum computation. Sci. Rep. 5, 7815 (2015)
Sheng, Y.B., Deng, F.G., Long, G.L.: Complete hyperentangled-Bell-state analysis for quantum communication. Phys. Rev. A 82, 032318 (2010)
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)
Wang, T.J., Lu, Y., Long, G.L.: Generation and complete analysis of the hyperentangled Bell state for photons assisted by quantum-dot spins in optical microcavities. Phys. Rev. A 86, 042337 (2012)
Liu, Q., Zhang, M.: Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators. Phys. Rev. A 91, 062321 (2015)
Xia, Y., Chen, Q.Q., Song, J., Song, H.S.: Efficient hyperentangled Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity. J. Opt. Soc. Am. B 29, 1029 (2012)
Wang, X.L., Cai, X.D., Su, Z.E., Chen, M.C., Wu, D., Li, L., Liu, N.L., Lu, C.Y., Pan, J.W.: Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518, 516–519 (2015)
Ren, B.C., Deng, F.G.: Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities. Laser Phys. Lett. 10, 115201 (2013)
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)
Wang, T.J., Liu, L.L., Zhang, R., Cao, C., Wang, C.: One-step hyperentanglement purification and hyperdistillation with linear optics. Opt. Express 23, 9284–9294 (2015)
Mi, S.C., Wang, C., Wang, T.J.: Hyperentanglement purification with linear optics assisted by W-states. Quantum Inf. Process. 14, 623–634 (2014)
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)
Ren, B.C., Long, G.L.: General hyperentanglement concentration for photon systems assisted by quantum dot spins inside optical microcavities. Opt. Express 22, 6547–6561 (2014)
Ren, B.C., Long, G.L.: Highly efficient hyperentanglement concentration with two steps assisted by quantum swap gates. Sci. Rep. 5, 16444 (2015)
Li, X.H., Ghose, S.: Hyperconcentration for multipartite entanglement via linear optics. Laser Phys. Lett. 11, 125201 (2014)
Li, X.H., Ghose, S.: Hyperentanglement concentration for time-bin and polarization hyperentangled photons. Phys. Rev. A 91, 062302 (2015)
Li, X.H., Ghose, S.: Efficient hyperconcentration of nonlocal multipartite entanglement via the cross-Kerr nonlinearity. Opt. Express 23, 3550–3562 (2015)
Cao, C., Wang, T.J., Mi, S.C., Zhang, R., Wang, C.: Nonlocal hyperconcentration on entangled photons using photonic module system. Ann. Phys. 369, 128–138 (2016)
Fan, L.L., Xia, Y., Song, J.: Efficient entanglement concentration for arbitrary less-hyperentanglement multi-photon W states with linear optics. Quantum Inf. Process. 13, 1967–1978 (2014)
Liu, H.J., Xia, Y., Song, J.: Efficient hyperentanglement concentration for N-particle Greenberger–Horne–Zeilinger state assisted by weak cross-Kerr nonlinearity. Quantum Inf. Process. 15, 2033–2052 (2016)
Li, T., Deng, F.G., Wang, G.Y., Long, G.L.: Deterministic error correction for nonlocal spatial polarization hyperentanglement. Sci. Rep. 6, 20677 (2016)
Kalamidas, D.: Linear optical scheme for error-free entanglement distribution and a quantum repeater. Phys. Rev. A 73, 054304 (2006)
Takesue, H.: Entangling time-bin qubits with a switch. Phys. Rev. A 89, 062328 (2014)
Chen, T.Y., Zhang, J., Boileau, J.C., Jin, X.M., Yang, B., Zhang, Q., Yang, T., Laflamme, R., Pan, J.W.: Experimental quantum communication without a shared reference frame. Phys. Rev. Lett. 96, 150504 (2006)
Honjo, T., Nam, S.W., Takesue, H., Zhang, Q., Kamada, H., Nishida, Y., Tadanaga, O., Asobe, M., Baek, B., Hadfield, R.H., Miki, S., Fujiwara, M., Sasaki, M., Wang, Z., Inoue, K., Yamamoto, Y.: Long-distance entanglement-based quantum key distribution over optical fiber. Opt. Express 16, 19118–19126 (2008)
Yamamoto, T., Hayashi, K., Oezdemir, S.K., Koashi, M., Imoto, N.: Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace. Nature Photon. 2, 488–491 (2008)
Ikuta, R., Ono, Y., Tashima, T., Yamamoto, T., Koashi, M., Imoto, N.: Efficient decoherence-free entanglement distribution over lossy quantum channels. Phys. Rev. Lett. 106, 110503 (2011)
Gu, B., Xu, F., Ding, L.G., Zhang, Y.N.: High-capacity three-party quantum secret sharing with hyperentanglement. Int. J. Theor. Phys. 51, 3559–3566 (2012)
Song, S.Y., Cao, Y., Sheng, Y.B., Long, G.L.: Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement. Quantum Inf. Process. 12, 381–393 (2013)
Fan, L.L., Yan, X., Song, J.: Efficient entanglement concentration for arbitrary less-hyperentanglement multi-photon W states with linear optics. Quantum Inf. Process. 13, 1967–1978 (2014)
Sheng, Y.B., Guo, R., Pan, J., Zhou, L., Wang, X.F.: Two-step measurement of the concurrence for hyperentangled state. Quantum Inf. Process. 14, 963–978 (2015)
Liu, D., Zong, Z.C., Ma, W.: High-capacity quantum secret sharing with hyperdense coding assisted by hyperentangled photon pairs. Int. J. Theor. Phys. 52, 2245–2254 (2013)
Wang, C., Ma, H.Q., Jiao, R.Z., Zhang, Y.: An improved quantum repeater protocol using hyperentangled state purification. Eur. Phys. J. D 64, 573–578 (2011)
Wang, H.B., Huang, Y.G., Fang, X., Gu, B., Fu, D.S.: High-capacity three-party quantum secret sharing with single photons in both the polarization and the spatial-mode degrees of freedom. Int. J. Theor. Phys. 52, 1043–1051 (2013)
Gu, B., Zhang, C.Y., Cheng, G.S., Huang, Y.G.: Robust quantum secure direct communication with a quantum one-time pad over a collective-noise channel. Sci. China Phys. Mech. Astron. 54, 942–947 (2011)
Lu, P.M., Xia, Y., Song, J.: Efficient W polarization state distribution over an arbitrary collective-noise channel with cross-Kerr nonlinearity. Opt. Commun. 284, 5866–5870 (2011)
Xia, Y., Fan, L.L., Hao, S.Y., He, J., Song, J., Wei, R.S., Huang, L.Q.: Efficient nonlocal entangled state distribution over the collective-noise channel. Quantum Inf. Process. 12, 3553–3568 (2013)
Lai, H., Orgun, M.A., Xiao, J.H., Xue, L.Y.: Fault-tolerant high-capacity quantum key distribution over a collective-noise channel using extended unitary operations. Quantum Inf. Process. 13, 1523–1535 (2014)
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, 1413–1424 (2014)
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, 361–372 (2015)
Xu, J.S., Li, C.F.: Quantum integrated circuit: classical characterization. Sci. Bull. 60, 141 (2015)
Ye, T.Y.: Quantum secure direct dialogue over collective noise channels based on logical Bell states. Quantum Inf. Process. 14, 1487–1499 (2015)
Dong, L., Wang, J.X., Li, Q.Y., Shen, H.Z., Dong, H.K., Xiu, X.M., Ren, Y.P., Gao, Y.J.: Quantum secure direct communication against the collective noise with polarization-entangled Bell states. Prog. Theor. Exp. Phys. 12, 123A02 (2015)
Huang, W., Wen, Q.Y., Liu, B., Gao, F.: Multi-user quantum key distribution with collective eavesdropping detection over collective-noise channels. Chin. Phys. B. 24, 070308 (2015)
Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grant Nos. 11674033 and 11474026 and the Fundamental Research Funds for the Central Universities under Grant No. 2015KJJCA01.
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Gao, CY., Wang, GY., Zhang, H. et al. Multi-photon self-error-correction hyperentanglement distribution over arbitrary collective-noise channels. Quantum Inf Process 16, 11 (2017). https://doi.org/10.1007/s11128-016-1482-x
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DOI: https://doi.org/10.1007/s11128-016-1482-x