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Hierarchical controlled remote preparation of an arbitrary m-qudit state with four-qudit cluster states

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Abstract

We present a general scheme for hierarchical controlled remote preparation of an arbitrary m-qudit state by using m four-qudit cluster states as the quantum channel. The sender first performs m-qudit positive operator-valued measurement in accordance with her knowledge of prepared state and then performs generalized X-basis measurements on her entangled particles. The upper-grade agent only needs perform unitary operation in accordance with one of the lower-grade agents’ measurement results for controlled remote preparation of an arbitrary m-qudit state. The lower-grade agent needs perform corresponding unitary operations in accordance with all the other agents’ measurement results. The protocol has the advantage of transmitting less entangled particles for hierarchical controlled remote preparation of an arbitrary m-qudit state via four-qudit cluster states.

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Data Availability Statement

The authors confirm that the data supporting the findings of this study are available within the article.

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)

    MathSciNet  MATH  ADS  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)

    ADS  Google Scholar 

  4. Zhang, Y.C., Chen, Z.Y., Pirandola, S., Wang, X.Y., Zhou, C., Chu, B.J., Zhao, Y.J., Xu, B.J., Yu, S., Guo, H.: Long-distance continuous-variable quantum key distribution over 202.81 km of fiber. Phys. Rev. Lett. 125(1), 010502 (2020)

    ADS  Google Scholar 

  5. Cao, Y., Li, Y.H., Yang, K.X., Jiang, Y.F., Li, S.L., Hu, X.L., Abulizi, M., Li, C.L., Zhang, W.J., Sun, Q.C., Liu, W.Y., Jiang, X., Liao, S.K., Ren, J.G., Li, H., You, L.X., Wang, Z., Yin, J., Lu, C.Y., Wang, X.B., Zhang, Q., Peng, C.Z., Pan, J.W.: Long-distance free-space measurement-device-independent quantum key distribution. Phys. Rev. Lett. 125(26), 260503 (2020)

    ADS  Google Scholar 

  6. Fang, X.T., Zeng, P., Liu, H., Zou, M., Wu, W., Tang, Y.L., Sheng, Y.J., Xiang, Y., Zhang, W.J., Li, H., Wang, Z., You, L.X., Li, M.J., Chen, H., Chen, Y.A., Zhang, Q., Peng, C.Z., Ma, X.F., Chen, T.Y., Pan, J.W.: Implementation of quantum key distribution surpassing the linear rate-transmittance bound. Nat. Photon. 14(7), 422 (2020)

    ADS  Google Scholar 

  7. 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)

    ADS  Google Scholar 

  8. Zhou, C., Wang, X., Zhang, Z., Yu, S., Chen, Z., Guo, H.: Rate compatible reconciliation for continuous-variable quantum key distribution using Raptor-like LDPC codes. Sci. China Phys. Mech. Astron. 64(6), 260311 (2021)

    ADS  Google Scholar 

  9. 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)

    MathSciNet  MATH  ADS  Google Scholar 

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

    MATH  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  13. 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)

    ADS  Google Scholar 

  14. 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)

    Google Scholar 

  15. 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)

    ADS  Google Scholar 

  16. 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)

    Google Scholar 

  17. 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)

    Google Scholar 

  18. 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)

    ADS  Google Scholar 

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

    Google Scholar 

  20. Yang, Y.G., Wang, Y.C., Yang, Y.L., Chen, X.B., Li, D., Zhou, Y.H., Shi, W.M.: Participant attack on the deterministic measurement-device-independent quantum secret sharing protocol. Sci. China Phys. Mech. Astron. 64(6), 260321 (2021)

    MATH  ADS  Google Scholar 

  21. Qi, Z., Li, Y., Huang, Y., Feng, J., Zheng, Y., Chen, X.: A 15-user quantum secure direct communication network. Light Sci. Appl. 10, 183 (2021)

    ADS  Google Scholar 

  22. Long, G.L., Zhang, H.R.: Drastic increase of channel capacity in quantum secure direct communication using masking. Sci. Bull. 66, 1267 (2021)

    Google Scholar 

  23. Zhou, L., Sheng, Y.B.: One-step device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron. 65(6), 250311 (2022)

    ADS  Google Scholar 

  24. Ying, J.W., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent one-step quantum secure direct communication. Chin. Phys. B 31, 120303 (2022)

    ADS  Google Scholar 

  25. Sheng, Y.B., Zhou, L., Long, G.L.: One-step quantum secure direct communication. Sci. Bull. 67, 367 (2022)

    Google Scholar 

  26. Liu, X., Luo, D., Lin, G.S., Chen, Z.H., Huang, C.F., Li, S.Z., Zhang, C.X., Zhang, Z.R., Wei, K.J.: Fiber-based quantum secure direct communication without active polarization compensation. Sci. China Phys. Mech. Astron. 12, 120311 (2022)

    Google Scholar 

  27. Shor, P.W.:Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual IEEE Symposium on Foundations of Computer Science, pp. 124-134.(1994)

  28. Long, G.L., Xiao, L.: Parallel quantum computing in a single ensemble quantum computer. Phys. Rev. A 69(5), 052303 (2004)

    MathSciNet  ADS  Google Scholar 

  29. Feng, G.R., Xu, G.F., Long, G.L.: Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett. 110(19), 190501 (2013)

    ADS  Google Scholar 

  30. Ren, B.C., Deng, F.G.: Hyper-parallel photonic quantum computation with coupled quantum dots. Sci. Rep. 4, 4623 (2014)

    Google Scholar 

  31. Ren, B.C., Wang, G.Y., Deng, F.G.: Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime. Phys. Rev. A 91(3), 032328 (2015)

    ADS  Google Scholar 

  32. Ren, B.C., Deng, F.G.: Robust hyperparallel photonic quantum entangling gate with cavity QED. Opt. Express 25(10), 10863–10873 (2017)

    ADS  Google Scholar 

  33. Li, T., Long, G.L.: Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities. Phys. Rev. A 94(2), 022343 (2016)

    ADS  Google Scholar 

  34. Li, T., Deng, F.G.: Error-rejecting quantum computing with solid-state spins assisted by low-optical microcavities. Phys. Rev. A 94(6), 062310 (2016)

    ADS  Google Scholar 

  35. Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Physically feasible three-level transitionless quantum driving with multiple Schrodinger dynamics. Phys. Rev. A 93(5), 052324 (2016)

    ADS  Google Scholar 

  36. Reimer, C., Sciara, S., Roztocki, P., Islam, M., Corts, 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, 148–153 (2019)

    Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  38. Yang, C.P., Chu, S.I., Han, S.: Efficient many-party controlled teleportation of multiqubit quantum information via entanglement. Phys. Rev. A 70, 022329 (2004)

    ADS  Google Scholar 

  39. Yuan, H., Zhang, G., Xie, C., Zhang, Z.: Improving the scheme of bidirectional controlled teleportation with a five-qubit composite GHZ-Bell state. Laser Phys. Lett. 19, 085204 (2022)

    ADS  Google Scholar 

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

    MATH  ADS  Google Scholar 

  41. 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)

    ADS  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  43. 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)

    ADS  Google Scholar 

  44. 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)

    MATH  Google Scholar 

  45. Ivanov, S.S., Vitanov, N.V.: High-fidelity local addressing of trapped ions and atoms by composite sequences of laser pulses. Opt. Lett. 36, 1275–1277 (2011)

    ADS  Google Scholar 

  46. Xu, H., Song, X.K., Wang, D., Ye, L.: Quantum sensing of control errors in three-level systems by coherent control techniques. Sci. China-Phys. Mech. Astron (2022). https://doi.org/10.1007/s11433-022-2034-5

    Article  Google Scholar 

  47. Hillery, M., Bu\(\check{z}\)ek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

  48. Ju, X.X., Zhong, W., Sheng, Y.B., Zhou, L.: Measurement-device-independent quantum secret sharing with hyper-encoding. Chin. Phys. B 31, 100302 (2022)

    ADS  Google Scholar 

  49. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2000)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  51. 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)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  54. Ye, M.Y., Zhang, Y.S., Guo, G.C.: Faithful remote state preparation using finite classical bits and a nonmaximally entangled state. Phys. Rev. A 69, 022310 (2004)

    ADS  Google Scholar 

  55. 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. 17, 298 (2018)

    MATH  ADS  Google Scholar 

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

    ADS  Google Scholar 

  57. Zha, X.W., Wang, M.R., Jiang, R.X.: Two forms schemes of deterministic remote state preparation for four-qubit cluster-type state. Int. J. Theor. Phys. 59(3), 960–973 (2020)

    MathSciNet  MATH  Google Scholar 

  58. Chaudhary, M., Fadel, M., Ilo-Okeke, E.O., Pyrkov, A.N., Ivannikov, V., Byrnes, T.: Remote state preparation of two-component Bose-Einstein condensates. Phys. Rev. A 103(6), 062417 (2021)

    MathSciNet  ADS  Google Scholar 

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

    ADS  Google Scholar 

  60. Xiang, G.Y., Li, J., Yu, B., Guo, G.C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2005)

    ADS  Google Scholar 

  61. 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)

    ADS  Google Scholar 

  62. Ra, Y.S., Lim, H.T., Kim, Y.H.: Remote preparation of three-photon entangled states via single-photon measurement. Phys. Rev. A 94, 042329 (2016)

    ADS  Google Scholar 

  63. Xia, Y., Song, J., Song, H.S.: Multiparty remote state preparation. J. Phys. B 40, 3719 (2007)

    ADS  Google Scholar 

  64. Nguyen, B.A., Kim, J.: Joint remote state preparation. J. Phys. B 41, 095501 (2008)

    ADS  Google Scholar 

  65. Adepoju, A.G., Falaye, B.J., Sun, G.H., Camacho-Nieto, O., Dong, S.H.: Joint remote state preparation (JRSP) of two-qubit equatorial state in quantum noisy channels. Phys. Lett. A 381, 581 (2017)

    ADS  Google Scholar 

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

    MathSciNet  MATH  ADS  Google Scholar 

  67. Hou, K., Wang, J., Yuan, H., Shi, S.H.: Multiparty-controlled remote preparation of two-particle state. Commun. Theor. Phys. 52, 848 (2009)

    MATH  ADS  Google Scholar 

  68. Wang, D., Ye, L.: Multiparty-controlled joint remote state preparation. Quantum Inf. Process. 12, 3223 (2013)

    MathSciNet  MATH  ADS  Google Scholar 

  69. Sun, S., Zhang, H.: Double-direction quantum cyclic controlled remote state preparation of two-qubit states. Quantum Inf. Process. 20, 211 (2021)

    MathSciNet  MATH  ADS  Google Scholar 

  70. Wang, X.W., Xia, L.X., Wang, Z.Y., Zhang, D.Y.: Hierarchical quantum-information splitting. Opt. Commun. 283, 1196 (2010)

    ADS  Google Scholar 

  71. Wang, X.W., Zhang, D.Y., Tang, S.Q., Xie, L.J.: Multiparty hierarchical quantum-information splitting. J. Phys. B 44, 035505 (2011)

    ADS  Google Scholar 

  72. Shukla, C., Pathak, A.: Hierarchical quantum communication. Phys. Lett. A 377, 1337 (2013)

    MathSciNet  MATH  ADS  Google Scholar 

  73. Shukla, C., Thapliyal, K., Pathak, A.: Hierarchical joint remote state preparation in noisy environment. Quantum Inf. Process. 16, 205 (2017)

    MathSciNet  MATH  ADS  Google Scholar 

  74. Chen, N., Yan, B., Chen, G., Zhang, M.J., Pei, C.X.: Deterministic hierarchical joint remote state preparation with six-particle partially entangled state. Chin. Phys. B 27, 090304 (2018)

    ADS  Google Scholar 

  75. Ma, P.C., Chen, G.B., Li, X.W., Zhan, Y.B.: Hierarchically controlled remote preparation of an arbitrary single-qubit state by using a four-qubit \(\chi \) entangled state. Quantum Inf. Process. 17, 105 (2018)

    MathSciNet  MATH  ADS  Google Scholar 

  76. Zha, X.W., Miao, N.: Hierarchical controlled quantum teleportation. Mod. Phys. Lett. B 33, 1950356 (2019)

    MathSciNet  ADS  Google Scholar 

  77. Bich, C.T., An, N.B.: Hierarchically controlling quantum teleportations. Quantum Inf. Process. 18, 245 (2019)

    MathSciNet  MATH  ADS  Google Scholar 

  78. Wang, N.N., Ma, S.Y., Li, X.: Hierarchical controlled quantum communication via the \(\chi \) state under noisy environment. Mod. Phys. Lett. A 35, 2050306 (2020)

    MathSciNet  MATH  ADS  Google Scholar 

  79. Barik, S., Warke, A., Behera, B.K., Panigrahi, P., Deterministic, K., hierarchical remote state preparation of a two-qubit entangled state using Brown, et al.: State in a noisy environment. IET Quantum Commun. 2, 49–54 (2020)

  80. Ma, S., Wang, N.: Hierarchical remote preparation of an arbitrary two-qubit state with multiparty. Quantum Inf. Process. 20, 276 (2021)

    MathSciNet  MATH  ADS  Google Scholar 

  81. Tang, J., Ma, S.Y., Li, Q.: Probabilistic hierarchical quantum information splitting of arbitrary multi-qubit states. Entropy 24, 1077 (2022)

    MathSciNet  Google Scholar 

  82. Kysela, J.: High-dimensional quantum Fourier transform of twisted light. Phys. Rev. A 104, 012413 (2021)

    ADS  Google Scholar 

  83. Shi, R.H., Mu, Y., Zhong, H., Cui, J., Zhang, S.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  85. Ma, P.C., Chen, G.B., Li, X.W., Zhan, Y.B.: Hierarchical controlled remote state preparation by using a four-qubit cluster state. Int. J. Theor. Phys. 57, 1748 (2018)

    MathSciNet  MATH  Google Scholar 

  86. Lu, X.Q., Feng, K.F., Li, X.W., Zhou, P.: Deterministic remote preparation of an arbitrary single-qudit state with high-dimensional spatial-mode entanglement via linear-optical elements. Int. J. Theor. Phys. 61, 36 (2022)

    MathSciNet  MATH  Google Scholar 

  87. Li, X.H., Ghose, S.: Control power in perfect controlled teleportation via partially entangled channels. Phys. Rev. A 90, 052305 (2014)

    ADS  Google Scholar 

  88. Duan, W.X., Wang, T.J.: Control power of high-dimensional controlled dense coding. Phys. Rev. A 105, 052417 (2022)

    MathSciNet  ADS  Google Scholar 

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Acknowledgements

This work was supported by the Natural Science Foundation of Guangxi under Grant No. 2018JJA110112 and National Natural Science Foundation of China under Grant Nos. 11564004 and 61501129.

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Authors and Affiliations

  1. College of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, People’s Republic of China

    Rui-Heng Jin, Wen-Shan Wei & Ping Zhou

  2. Key lab of quantum information and quantum optics, Guangxi University for Nationalities, Nanning, 530006, People’s Republic of China

    Rui-Heng Jin, Wen-Shan Wei & Ping Zhou

  3. Guangxi Key Laboratory of Hybrid Computational and IC Design Analysis, Nanning, 530006, People’s Republic of China

    Ping Zhou

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Jin, RH., Wei, WS. & Zhou, P. Hierarchical controlled remote preparation of an arbitrary m-qudit state with four-qudit cluster states. Quantum Inf Process 22, 113 (2023). https://doi.org/10.1007/s11128-023-03855-z

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