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Controlled Cyclic Remote Preparation of an Arbitrary Single-Qudit State by Using a Seven-Qudit Cluster State as the Quantum Channel

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Abstract

We present a protocol for controlled cyclic remote preparation of an arbitrary single-qudit state via a seven-qudit cluster state. In the protocol, Alice can help the remote agent Bob prepare an arbitrary single-qudit state, Bob can help the agent Charlie prepare an arbitrary single-qudit state and at the same time Charlie can help Alice prepare an arbitrary single-qudit state under the controller David’s control. Alice, Bob and Charlie first perform positive operator-valued measurement (POVM) on their entangled particles according to the information of the prepared state, then perform generalized X-basis measurement. The controller performs generalized X-basis measurement on his entangled particle. The arbitrary single-qudit states can be cyclic remote prepared under the controller’s control. The protocol is more convenient in application since it only requires single-particle measurement and single-particle unitary operations for controlled cyclic remote preparation of the single-qudit states.

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References

  1. Bennett, C.H., Brassad, 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, pp 175–179. IEEE Press, New York (1984)

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Leverrier, A.: Security of continuous-variable quantum key distribution via a Gaussian de Finetti reduction. Phys. Rev. Lett. 118(20), 200501 (2017)

    Article  ADS  Google Scholar 

  4. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65(3), 032302 (2002)

    Article  ADS  Google Scholar 

  5. 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 (4), 042317 (2003)

    Article  ADS  Google Scholar 

  6. 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(9), e16144 (2016)

    Article  Google Scholar 

  7. 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(22), 220501 (2017)

    Article  ADS  Google Scholar 

  8. Chen, S.S., Zhou, L., Zhong, W., Sheng, Y.B.: Three-step three-party quantum secure direct communication. Sci. China Phys. Mech. Astron. 61 (9), 090312 (2018)

    Article  Google Scholar 

  9. 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. Quantum Eng. 1, 26 (2019)

    Article  Google Scholar 

  10. Qi, R.Y., Sun, Z., Lin, Z.S., Niu, P.H., Hao, W.T., Song, L.Y., Huang, Q., Gao, J.C., Yin, L.G., Long, G.L.: Implementation and security analysis of practical quantum secure direct communication. Light Sci. Appl. 8, 22 (2019)

    Article  ADS  Google Scholar 

  11. 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 

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

    Article  ADS  Google Scholar 

  13. Barreiro, J.T., Wei, T.C., Kwiat, P.G.: Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 4(4), 282 (2008)

    Article  Google Scholar 

  14. Long, G.F., Feng, G.R., Sprenger, P.: Overcoming synthesizer phase noise in quantum sensing. Quantum Eng. 1, 27 (2019)

    Article  Google Scholar 

  15. Żukowski, M., Zeilinger, A., Horne, M.A., Ekert, A.K.: Event-ready-detectors Bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287 (1993)

    Article  ADS  Google Scholar 

  16. Bose, S., Vedral, V., Knight, P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A 57, 822 (1998)

    Article  ADS  Google Scholar 

  17. Zhou, P., Deng, F.G., Zhou, H.Y.: Probabilistic quantum entanglement swapping and quantum secret sharing with high-dimensional pure entangled systems. Phys. Scr. 79, 035005 (2009)

    Article  ADS  MATH  Google Scholar 

  18. Su, X.L., Tian, C.X., Deng, X.W., Li, Q., Xie, C.D., Peng, K.C.: Quantum entanglement swapping between two multipartite entangled states. Phys. Rev. Lett. 117, 240503 (2016)

    Article  ADS  Google Scholar 

  19. 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 

  20. Pan, J.W., Simon, C., Brukne, C., Zellinger, A.: Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001)

    Article  ADS  Google Scholar 

  21. 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 

  22. 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 

  23. 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)

    Article  ADS  Google Scholar 

  24. 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 

  25. Li, T., Yang, G.J., Deng, F.G.: Heralded quantum repeater for a quantum communication network based on quantum dots embedded in optical microcavities. Phys. Rev. A 93, 012302 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. Pan, J., Zhou, L., Gu, S.P., Wang, X.F., Sheng, Y.B., Wang, Q.: Efficient entanglement concentration for concatenated Greenberger-Horne-Zeilinger state with the cross-Kerr nonlinearity. Quantum Inf. Process. 15, 1669–1687 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  29. Ren, B.C., Wang, H., Alzahrani, F., Hobiny, A., Deng, F.G.: Hyperentanglement concentration of nonlocal two-photon six-qubit systems with linear optics. Ann. Phys. 385, 86–94 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. 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 

  31. Huelga, S.F., Vaccaro, J.A., Chefles, A., Plenio, M.B.: Quantum remote control: Teleportation of unitary operations. Phys. Rev. A 63, 042303 (2001)

    Article  ADS  MATH  Google Scholar 

  32. Huelga, S.F., Plenio, M.B., Vaccaro, J.A.: Remote control of restricted sets of operations: Teleportation of angles. Phys. Rev. A 65, 042316 (2002)

    Article  ADS  Google Scholar 

  33. Wang, A.M.: Remote implementations of partially unknown quantum operations of multiqubits. Phys. Rev. A 74, 032317 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  34. Hu, S., Cui, W.X., Wang, D.Y., Bai, C.H., Guo, Q., Wang, H.F., Zhu, A.D., Zhang, S.: Teleportation of a Toffoli gate among distant solid-state qubits with quantum dots embedded in optical microcavities. Sci. Rep. 5, 11321 (2015)

    Article  ADS  Google Scholar 

  35. Lin, J.Y., He, J.G., Gao, Y.C., Li, X.M., Zhou, P.: Bidirectional controlled remote implementation of an arbitrary single qubit unitary operation with EPR and cluster states. Int. J. Theor. Phys. 56, 1085–1095 (2017)

    Article  MATH  Google Scholar 

  36. Jiao, X.F., Zhou, P., lv, S.X.: Remote implementation of single-qubit operations via hyperentangled states with cross-Kerr nonlinearity. J. Opt. Soc. Am. B 36, 867–875 (2019)

    Article  ADS  Google Scholar 

  37. 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 

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

    Article  ADS  MATH  Google Scholar 

  39. Xiao, X., Yao, Y., Zhong, W.J., Li, Y.L., Xie, Y.M.: Enhancing teleportation of quantum Fisher information by partial measurements. Hys. Rev. A 93, 012307 (2016)

    Article  ADS  Google Scholar 

  40. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A63, 014302 (2000)

    Article  ADS  Google Scholar 

  41. Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)

    Article  ADS  Google Scholar 

  42. 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 

  43. Xin, T., Hao, L., Hou, S.Y., Feng, G.R., Long, G.L.: Preparation of pesudo-pure states for NMR quantum computing with one ancilary qubit. Sci. China Phys. Mech. Astron. 62, 960312 (2019)

    Article  ADS  Google Scholar 

  44. Devetak, I., Berger, T.: Low-entanglement remote state preparation. Phys. Rev. Lett. 87, 197901 (2001)

    Article  ADS  Google Scholar 

  45. Leung, D.W., Shor, P.W.: Oblivious remote state preparation. Phys. Rev. Lett. 90, 127905 (2003)

    Article  ADS  Google Scholar 

  46. Berry, D.W., Sanders, B.C.: Optimal remote state preparation. Phys. Rev. Lett. 90, 057901 (2003)

    Article  ADS  Google Scholar 

  47. Ye, M.Y., Zhang, Y.S., Guo, G.C.: Faithful remote state preparation using finite classical bits and a nonmaximally entangled state. Phys. Rev. A69, 022310 (2004)

    Article  ADS  Google Scholar 

  48. Wei, J.H., Shi, L., Ma, L.H., Xue, Y., Zhuang, X.C., Kang, Q.Y., Li, X.S.: Remote preparation of an arbitrary multi-qubit state via two-qubit entangled states. Quantum Inf. Process. 16, 260 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. Zhou, P., Jiao, X.F., Lv, S.X.: Parallel remote state preparation of arbitrary single-qubit states via linear- optical elements by using hyperentangled Bell states as the quantum channel. Quantum Inf. Process. 298, 17 (2018)

    MATH  Google Scholar 

  50. Nawaz, M., Islam, R., Ikram, M.: Remote state preparation through hyperentangled atomic states. J. Phys. B. 51, 075501 (2018)

    Article  ADS  Google Scholar 

  51. Peng, X.H., Zhu, X.W., Fang, X.M., Feng, M., Liu, M.L., Gao, K.L.: Experimental implementation of remote state preparation by nuclear magnetic resonance. Phys. Lett. A 271, 306 (2003)

    Google Scholar 

  52. Wu, W., Liu, W.T., Chen, C.Z., Li, P.X.: Deterministic remote preparation of pure and mixed polarization states. Phys. Rev. A 81, 042301 (2010)

    Article  ADS  Google Scholar 

  53. Barreiro, J.T., Wei, T.C., Kwiat, P.G.: Remote preparation of single-photon hybrid entangled and vector-polarization states. Phys. Rev. Lett. 105, 030407 (2010)

    Article  ADS  Google Scholar 

  54. Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910 (2001)

    Article  ADS  Google Scholar 

  55. Zhou, D.L., Zeng, B., Xu, Z., Sun, C.P.: Quantum computation based on d-level cluster states. Phys. Rev. A 68, 062303 (2003)

    Article  ADS  Google Scholar 

  56. Walther, P., Aspelmeyer, M., Resch, K.J., Zeilinger, A.: Experimental violation of a cluster state Bell inequality. Phys. Rev. Lett. 95, 020403 (2005)

    Article  ADS  Google Scholar 

  57. Vallone, G., Pomarico, E., Mataloni, P., Martini, F.D., Berardi, V.: Realization and characterization of a 2-photon 4-qubit linear cluster state. Phys. Rev. Lett. 98, 180502 (2007)

    Article  ADS  Google Scholar 

  58. Ceccarelli, R., Vallone, G., Martini, F.D., 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 

  59. Zha, X.W., Song, H.Y.: Remote preparation of a two-particle state using a four-qubit cluster state. Opt. Commun. 284, 1472 (2011)

    Article  ADS  Google Scholar 

  60. Lu, Q.C., Liu, D.P., He, Y.H., Liao, Y.M., Qin, X.C., Qin, J.S., Zhou, P.: Linear-optics-based bidirectional controlled remote state preparation via five-photon cluster-type states for quantum communication network. Int. J. Theor. Phys. 55, 535 (2016)

    Article  MATH  Google Scholar 

  61. Reimer, C., Sciara, S., Roztocki, P., Islam, M., Cortes, L.R., Zhang, Y.B., Fischer, B., Loranger, S., Kashyap, R., Cino, A., Chu, S.T., Little, B.E., Moss, D.J., Caspani, L., Munro, W.J., Azana, J., Kues, M., Morandotti, R.: High-dimensional one-way quantum processing implemented on d-level cluster states. Nat. Phys. 15, 148 (2019)

    Article  Google Scholar 

  62. Du, Z.L., Li, X.L.: Deterministic joint remote state preparation of four-qubit cluster type with tripartite involvement. Quantum Inf. Process. 39, 19 (2020)

    MathSciNet  Google Scholar 

  63. Sk, R., Baishya, A., Behera, B.K., Panigrahi, P.K.: Experimental realization of quantum teleportation of an arbitrary two-qubit state using a four-qubit cluster state. Quantum Inf. Process. 87, 19 (2020)

    Google Scholar 

  64. Jiang, M., Jiang, F.: Deterministic joint remote state preparation of arbitrary multi-qudit states. Phys. Lett. A 377, 2524 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  65. Jiang, D., Chen, Y.Y., Gu, X.M., Xie, L., Chen, L.J.: Deterministic secure quantum communication using a single d-level system. Sci. Rep. 7, 44934 (2017)

    Article  ADS  Google Scholar 

  66. Fonseca, A.: High-dimensional quantum teleportation under noisy environments. Phys. Rev. A 100, 062311 (2019)

    Article  ADS  Google Scholar 

  67. Ren, B.C., Long, G.L.: General hyperentanglement concentration for photon systems assisted by quantum dot spins inside optical microcavities. Opt. Express 22, 6547 (2014)

    Article  ADS  Google Scholar 

  68. Gao, C.Y., Ren, B.C., Zhang, Y.X., Ai, Q., Deng, F.G.: The linear optical unambiguous discrimination of hyperentangled bell states assisted by time bin. Ann. Phys. 531, 1900201 (2019)

    Article  MathSciNet  Google Scholar 

  69. Guo, P.L., Dong, C., He, Y., Jing, F., He, W.T., Ren, B.C., Li, C.Y., Deng, F.G.: Efficient quantum key distribution against collective noise using polarization and transverse spatial mode of photons. Opt. Express 28, 4611 (2020)

    Article  ADS  Google Scholar 

  70. Guo, Y., Hu, X.M., Liu, B.H., Huang, Y.F., Li, C.F., Guo, G.C.: Experimental realization of path-polarization hybrid high-dimensional pure state. Opt. Express 26, 28918 (2018)

    Article  ADS  Google Scholar 

  71. Hu, X.M., Xing, W.B., Liu, B.H., Huang, Y.F., Li, C.F., Guo, G.C.: Efficient generation of high-dimensional entanglement through multipath down-conversion. Phys. Rev. Lett. 125, 090503 (2020)

    Article  ADS  Google Scholar 

  72. Hu, X.M., Xing, W.B., Liu, B.H., He, D.Y., Cao, H., Guo, Y., Zhang, C., Zhang, H., Huang, Y.F., Li, C.F., Guo, G.C.: Efficient distribution of high-dimensional entanglement through 11 km fiber. Optica 7, 738 (2020)

    Article  ADS  Google Scholar 

  73. Hu, X.M., Zhang, C., Liu, B.H., Cao, Y., Ye, X.J., Guo, Y., Xing, W.B., Huang, C.X., Huang, Y.F., Li, C.F., Guo, G.C.: Experimental high-dimensional quantum teleportation. Phys. Rev. Lett. 125, 230501 (2020)

    Article  ADS  Google Scholar 

  74. Hu, X.M., Guo, Y., Liu, B.H., Huang, Y.F., Li, C.F., Guo, G.C.: Beating the channel capacity limit for superdense coding with entangled ququarts. Sci. Adv. 4, eaat9304 (2018)

    Article  ADS  Google Scholar 

  75. Chen, Y.X., Du, J., Liu, S.Y., Wang, X.H.: Cyclic quantum teleportation. Quantum Inf. Process. 16, 201 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  76. Sang, Z.W.: Cyclic controlled teleportation by using a seven-qubit entangled state. Int. J. Theor. Phys. 57, 3835 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  77. Sang, Z.W.: Cyclic controlled joint remote state preparation by using a ten-qubit entangled state. Int. J. Theor. Phys. 58, 255 (2019)

    Article  MATH  Google Scholar 

  78. Shao, Z.L., Long, Y.X.: Circular controlled quantum teleportation by a genuine seven-qubit entangled state. Int. J. Theor. Phys. 58, 1957 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  79. Peng, J.Y., He, Y.: Cyclic controlled remote implementation of partially unknown quantum operations. Int. J. Theor. Phys. 58, 3065 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  80. Shi, J., Zhang, X., Zhu, Y.: Cyclic controlled quantum teleportation using three-dimensional hyper-entangled state. Int. J. Theor. Phys. 58, 3036 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  81. 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, 1541 (2019)

    Article  MATH  Google Scholar 

  82. Gu, J., 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, 200 (2020)

    Article  MATH  Google Scholar 

  83. Sun, S.Y., Li, L.X., Zhang, H.S.: Quantum cyclic controlled teleportation of unknown states with arbitrary number of qubits by using seven-qubit entangled channel. Int. J. Theor. Phys. 59, 1017 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  84. Sun, S.Y., Zhang, H.S.: Quantum double-direction cyclic controlled communication via a thirteen-qubit entangled state. Quantum Inf. Process. 19, 120 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  85. Yang, X., Bai, M.Q., Mo, Z.W., Xiang, Y.: Bidirectional and cyclic quantum dense coding in a high-dimension system. Quantum Inf. Process. 19, 43 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  86. Zhang, C.Y., Bai, M.Q.: Multi-hop cyclic joint remote state preparation. Int. J. Theor. Phys. 59, 1277 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  87. Zeng, B., Zhang, P.: Remote-state preparation in higher dimension and the parallelizable manifold sn− 1. Phys. Rev. A 65, 022316 (2002)

    Article  ADS  Google Scholar 

  88. Liao, Y.M., Zhou, P., Qin, X.C., He, Y.H., Qin, J.S.: Controlled remote preparing of an arbitrary two-qudit state with two-particle entanglements and positive operator-valued measure. Commun. Theor. Phys. 61, 315 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11564004 and 61501129, Natural Science Foundation of Guangxi under Grant No. 2018JJA110112, the Special Funds of Guangxi Distinguished Experts Construction Engineering and Xiangsihu Young Scholars and Innovative Research Team of GXUN.

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Li, Y.H., He, L.M. & Zhou, P. Controlled Cyclic Remote Preparation of an Arbitrary Single-Qudit State by Using a Seven-Qudit Cluster State as the Quantum Channel. Int J Theor Phys 60, 1635–1649 (2021). https://doi.org/10.1007/s10773-021-04786-0

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