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Double-Direction Cyclic Controlled Remote Implementation of Partially Known Quantum Operations

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Abstract

The purpose of this paper is to study the double directional cyclic controlled remote implementation (DDCCRI) of partially known quantum operations. We construct entangled channels with 13-, 19- and 16-qubits through Hadamard gates and controlled-NOT gates, respectively. Based on these quantum channels that we construct, two novel theoretical schemes are proposed to implement four-party DDCCRI with partially known single-qubit and two-qubit operations, respectively, and then we give four-party asymmetric scheme for DDCCRI with partially known single-qubit and two-qubit operations. For any of these three schemes, each correspondent can implement two partially known operations on two remote systems of the other two correspondents, respectively and synchronously under the control of the supervisor, thus achieving four-party cyclic controlled remote implementation in clockwise and counterclockwise directions simultaneously. Furthermore, the presented three schemes for four-party DDCCRI can be generalized into the case with n (n > 3) correspondents. In our schemes, the unified analytical formulas for the manipulations of the senders, supervisor and receivers are given, and the success probability of each proposed schemes can reach 100%, and only specific two-qubit projective measurements, single-qubit von Neumann measurements, Hadamard gate, CNOT gate and Pauli gates are required in this article, which can be easily executed in physics. We also discuss the intrinsic efficiency and the security of the presented schemes.

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Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Bennett, C.H., Brassard, G.: Quantum cryptography: Public Key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, pp 175–179. IEEE Press, Bangalore (1984)

  2. Zhang, C.M., Song, X.T., Treeviriyanupab, P., et al.: Delayed error verification in quantum key distribution. Chin. Sci. Bull. 59(23), 2825–2828 (2014)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Hao, L., Li, J.L., Long, G.L.: Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution. Sci. China-Phys. Mech. Astron. 53(3), 491–495 (2010)

    Article  ADS  Google Scholar 

  5. Peng, J.Y., Bei, M.Q., Mo, Z.W.: Bidirection quantum states sharing. Int. J. Theor. Phys. 55, 2481–2489 (2016)

    Article  MATH  Google Scholar 

  6. Chang, Y., Xu, C.X., Zhang, S.B., et al.: Controlled quantum secure direct communication and authentication protocol based on five-particle cluster state and quantum one-time pad. Chin. Sci. Bull. 59(21), 2541–2546 (2014)

    Article  Google Scholar 

  7. Bennett, C.H., Brassard, G., Crépeau, C, et al.: 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 

  8. Peng, J.Y., Bai, M.Q., Mo, Z.W.: Deterministic multi-hop controlled teleportation of arbitrary single-qubit state. Int. J. Theor. Phys. 56, 3348–3358 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, Z.Y., Song, J.F.: Controlled remote prepartion of a two-qubit state via positive operator-valued measure and two three-qubit entanglements. Int. J. Theor. Phys. 50, 2410 (2011)

    Article  MATH  Google Scholar 

  10. Peng, J.Y.: Remote preparation of general one-, two- and three-qubit states via χ-type entangled states. Int. J. Theor. Phys. 59(12), 3789–3803 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  11. Murao, M., Vedral, V.: Remote information concentration using a bound entangled state. Phys. Rev. Lett. 86, 352–356 (2001)

    Article  ADS  Google Scholar 

  12. Peng, J.Y., Lei, H.X., Mo, Z.W.: Faithful remote information concentration based on the optimal universal 1 ⟶ 2 telecloning of arbitrary two-qubit states. Int. J. Theor. Phys. 53, 1637–1647 (2014)

    Article  MATH  Google Scholar 

  13. Huelga, S.F., Vaccaro, J.A., Chefles, A., et al.: Quantum remote control: teleportation of unitary operations. Phys. Rev. A 63(4), 042303 (2001)

    Article  ADS  MATH  Google Scholar 

  14. Peng, J.Y., Bei, M.Q., Mo, Z.W.: Multicharacters remote rotation sharing with five-particle cluster state. Quantum Inf. Process. 18, 339 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  15. Huelga, S.F., Plenio, M., Vaccaro, J.A.: Remote control of restricted sets of operations: Teleportation of angles. Phys. Rev. A 65(4), 042316 (2002)

    Article  ADS  Google Scholar 

  16. Zou, X.B., Pahlke, K., Mathis, W.: Teleportation implementation of nondeterministic quantum logic operations by using linear optical elements. Phys. Rev. A 65(6), 64305–64305 (2002)

    Article  ADS  Google Scholar 

  17. Dür, W., Vidal, G., Cirac, J.: Optimal conversion of non-local unitary operations. Phys. Rev. Lett. 89(5), 057901 (2002)

    Article  ADS  Google Scholar 

  18. Zhang, Y.S., Ye, M.Y., Guo, G.C.: Conditions for optimal construction of two-qubit non-local gates. Phys. Rev. A 71(6), 062331 (2005)

    Article  ADS  Google Scholar 

  19. Wang, A.M.: Remote implementations of partially unknown quantum operations of multiqubits. Phys. Rev. A 74(3), 396–401 (2005)

    MathSciNet  Google Scholar 

  20. Wang, A.M.: Combined and controlled remote implementations of partially unknown quantum operations of multiqubits using Greenberger-Horne-Zeilinger states. Phys. Rev. A 75(6), 062323 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zhao, N.B., Wang, A.M.: Local implementation of nonlocal operations with block forms. Phys. Rev. A 78(1), 014305 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Zhang, Z.J., Cheung, C.Y.: Shared quantum remote Control: quantum operation sharing. J. Phys. B: At. Mol. Opt. Phys. 44, 165508 (2011)

    Article  ADS  Google Scholar 

  23. Ye, B.L., Liu, Y.M., Liu, X.S., Zhang, Z.J.: Remotely sharing a single-qubit operation with a five-qubit genuine state. Chin. Phys. Lett. 30(2), 020301 (2013)

    Article  ADS  Google Scholar 

  24. Hassanpour, S., Houshmand, M.: Bidirectional teleportation of a pure EPR state by using GHZ states. Quantum Inf. Process. 15(2), 905–912 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Peng, J.Y., Xiang, Y.: Bidirectional remote state preparation in noisy environment assisted by weak measurement. Optics Commun. 499, 127285 (2021)

    Article  Google Scholar 

  26. Zhou, R.G., Zhang, Y.N.: Bidirectional quantum controlled teleportation by using GHZ state. Int. J. Theor. Phys. 58(10), 3594–3601 (2019)

    Article  MATH  Google Scholar 

  27. Yang, Y.Q., Zha, X.W., Yu, Y.: Asymmetric bidirectional controlled teleportation via seven-qubit cluster state. Int. J. Theor. Phys. 55(10), 4197–4204 (2016)

    Article  MATH  Google Scholar 

  28. Peng, J.Y., Bai, M.Q., Mo, Z.W.: Bidirectional controlled joint remote state preparation. Quantum Inf. Process 14, 4263–4278 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Wang, X., Mo, Z.W.: Bidirectional controlled joint remote state preparation via a seven-qubit entangled state. Int. J. Theor. Phys. 56, 1052 (2017)

    Article  MATH  Google Scholar 

  30. Zhou, S.Q., Bai, M.Q., Liao, T., et al.: Bidirectional quantum operation teleportation with different states. Int. J. Quantum Inf. 16(5), 1850042 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  31. Yuan, H., Yang, H.: Optimized bidirectional quantum operation teleportation with three Bell states. Int. J. Theor. Phys. 59(8), 1–8 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  32. He, Y.H., Lu, Q.C., Liao, Y.M., et al.: Bidirectional controlled remote implementation of an arbitrary single qubit unitary operation with EPR and cluster states. Int. J. Theor. Phys. 54(5), 1726–1736 (2015)

    Article  MATH  Google Scholar 

  33. Sang, Z.W.: Cyclic controlled teleportation by using a seven-qubit entangled state. Int. J. Theor. Phys. 57(12), 3835–3838 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  34. Jiayin, P., He, Y.: Annular controlled teleportation. Intern. J. Theor. Phys. 58, 3271–3281 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  35. Li, Y.H., Qiao, Y., Sang, M.H., Nie, Y.Y.: Controlled cyclic quantum teleportation of an arbitrary two-qubit entangled state by using ten-qubit entangled state. Int. J. Theor. Phys. 58(5), 1541–1545 (2019)

    Article  MATH  Google Scholar 

  36. Peng, J.Y., Lei, HX.: Cyclic remote state preparation. Int. J. Theor. Phys. 60, 1593–160 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  37. Wang, M.M., Yang, C., Mousoli, R.: Controlled cyclic remote state preparation of arbitrary qubit states. CMC-Comput. Mater. Contin. 55, 321–329 (2018)

    Google Scholar 

  38. Peng, J.Y., He, Y.: Cyclic controlled remote implementation of partially unknown quantum operations. Int. J. Theor. Phys. 58(5), 3065–3072 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  39. Peng, J., Lei, H.: Cyclic remote implementation of partially unknown quantum operations. Chin. J. Electron. 30(2), 378–383 (2021)

    Article  Google Scholar 

  40. Jiang, S.X., Zhou, R.G., Xu, R.Q., Luo, G.F.: Cyclic hybrid double-channel quantum communication via Bell-state and GHZ-state in noisy environments. IEEE Access 7, 80530–80541 (2019)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  43. Yuan, H., Liu, Y.M., Zhang, W., Zhang, Z.J.: Optimizing resource consumption, operation complexity efficiency in quantum-state sharing. J. Phys. B: At. Mol. Opt. Phys. 41, 145506 (2008)

    Article  ADS  Google Scholar 

  44. Yang, C., Guo, G.C.: Disentanglement-free state of two pairs of two-level atoms. Phys. Rev. A 59, 4217 (1999)

    Article  ADS  Google Scholar 

  45. 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 

  46. Boschi, D., Branca, S., Martini, F.D., Hardy, L., Popescu, S.: Experimental realization of teleporting an unknown pur quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80, 1121 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. Riebe, M., et al.: Deterministic quantum teleportation with atoms. Nature 429, 734 (2004)

    Article  ADS  Google Scholar 

  48. Ikram, M., Zhu, S.Y., Zubairy, M.S.: Quantum teleportation of an entangled state. Phys. Rev. A 62, 022307 (2000)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No.11671284).

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Authors and Affiliations

  1. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu, 610068, China

    Jia-yin Peng, Zhen Yang & Liang Tang

  2. Research Center of Sichuan Normal University, National-Local Joint Engineering Laboratory of System Credibility Automatic Verification, Chengdu, 610068, China

    Jia-yin Peng, Zhen Yang & Liang Tang

  3. School of Mathematics and Information Science, Neijiang Normal University, Sichuan Neijiang, 641100, China

    Jia-yin Peng

  4. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610068, China

    Zhen Yang & Liang Tang

  5. Institute of Economics, Yunnan University of Finance and Economics, Kunming, 650221, China

    Jia-sheng Peng

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  1. Jia-yin Peng
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Contributions

Conceptually, all authors contributed equally in technical discussion and solution formulation. Specific contributions are as follows. The first author generated the initial idea and took the lead role in writing the manuscript. The second author computed all the intermediate steps. The third author wrote main content. The fourth author checked the computational process and reviewed all content of manuscript.

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Correspondence to Liang Tang.

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Peng, Jy., Yang, Z., Tang, L. et al. Double-Direction Cyclic Controlled Remote Implementation of Partially Known Quantum Operations. Int J Theor Phys 61, 256 (2022). https://doi.org/10.1007/s10773-022-05213-8

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