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Multi-type-output Assisted Cloning of Unknown Single-qubit States

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Abstract

Fusing the ideas of quantum multicast communication and quantum assisted cloning, we propose a scheme for two-type-output assisted cloning of arbitrary unknown single-qubit states, which can synchronously output accurate copies and orthogonal-complement copies of two different arbitrary unknown single-qubit states with a minimal assistance from a state preparer. In this scheme, a four-qubit maximally entangled cluster channel, classical communication, and several local quantum gates are employed. Quantum teleportation is required in the first stage of the scheme and in the second stage, the state preparer disentangles the left over entangled states by a two-qubit projective measurement process and conveys some classical messages to different parties so that accurate copies or orthogonal-complement copies are produced. To produce more copies or orthogonal-complement copies in the two-type-output assisted cloning scheme, we discuss our scheme for producing two copies and three copies of each unknown single-qubit state and suggest how to generalise this to N copies and orthogonal-complement copies of each unknown single-qubit state using the product of two multi-qubit GHZ-type states as quantum channel. In addition, by using the product of N EPR pairs as the quantum channel, the two-type-output assisted cloning scheme for arbitrary unknown single-qubit states is extended to the case of N-type-output (\(N\ge 3\)) to meet the needs of the development of quantum networks.

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References

  1. Kollmitzer, C., Pivk, M.: Applied quantum cryptogaraphy. Springer, Heidelberg (2010)

    Book  Google Scholar 

  2. Bennett, C. H., Brassard, G., Crepeau, et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)

  3. Peng, J.Y., He, Y.: Annular controlled teleportation. Int. J. Theor. Phys. 58, 3271–3281 (2019)

    Article  MathSciNet  Google Scholar 

  4. Zhou, P., Li, H.X., Deng, F.G., et al.: Multiparty-controlled teleportation of anarbitrary m-qudit state witha pure entangled quantum channel. J. Phys. A: Math. Theor. 40, 13121 (2007)

    Article  ADS  Google Scholar 

  5. Peng, J.Y., Tang, L., Yang, Z., et al.: Cyclic teleportation in noisy chanel with nondemolition parity analysis and weak measurement. Quantum Inf. Process. 210, 114 (2022)

    Article  ADS  Google Scholar 

  6. Lo, H.K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012)

    Article  ADS  PubMed  Google Scholar 

  7. Huang, W.: Improved multiparty quantum key agreement in travelling mode. Sci. China Physics, Mech. Astron. 59(12), 120311 (2016)

  8. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2001)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  10. Li, J.F., Liu, J.M., Feng, X.L., et al.: Deterministic remote two-qubit state preparation in dissipative environments. Quantum Inf. Process. 15, 2155–2168 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  11. Peng, J.Y., Bai, M.Q., Tang, L., et al.: Perfect controlled joint remote state preparation of arbitrary multi-qubit states independent of entanglement degree of the quantum channel. Quantum Inf. Process. 20, 340 (2021)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

  13. Peng, J.Y., Mo, Z.W.: Quantum sharing an unknown multi-particle state via POVM. Int. J. Theor. Phys. 52(2), 620–633 (2013)

    Article  Google Scholar 

  14. Shi, R.H., Huang, L.S., Yang, W., et al.: Asymmetric multi-party quantum state sharing of an arbitrary m-qubit state. Quantum Inf. Process. 10, 53–61 (2011)

    Article  MathSciNet  Google Scholar 

  15. Peng, J.Y., Bai, M.Q., Mo, Z.W.: Hierarchical and probabilistic quantum state sharing via a non-maximally entangled \(|\chi \rangle \)state. Chinese Physics B 23, 010304 (2014)

    Article  ADS  Google Scholar 

  16. Lai, H., Pieparzyk, J., Luo, M.X., et al.: High-capacity (2,3) threshold quantum secret sharing based on asymmetric quantum lossy channels. Quantum Inf. Process. 19, 157 (2020)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  18. Pati, A.K.: “Assisted cloning” and “orthogonal-complementing” of an unknown state. Phys. Rev. A 16, 022308 (2000)

  19. Scarani, V., Lblisdir, S., Gisin, N., et al.: Quantum cloning. Rev. Mod. Phys. 77, 1225 (2005)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. Han, L.F., Yuan, H., Yang, M., et al.: Assisted cloning of an arbitrary unknown tow-qubit state via agenuine four-qubit entangled state and positive operator-value measure. Indian J. Pure Appl. Phys. 52, 563–570 (2014)

    Google Scholar 

  21. Murao, M., Vedral, V.: Remote information concentration using a bound entangled state[J]. Phys. Rev. Lett. 86(2), 352–355 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  22. Peng, J.Y., Luo, M.X., Mo, Z.W.: Remote information concentration via four-particle cluster state and by positive operator-value measurement. International Journal of Modern Physics B 27(18), 1350091 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  23. Peng, J.Y., Lei, H.X., Mo, Z.W.: Faithful remote information concentration based on the optimal universal \(1\rightarrow 2\) telecloning of arbitrary two-qubit states. Int. J. Theor. Phys. 53(5), 1637–1647 (2014)

    Article  Google Scholar 

  24. Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299(5886), 802–803 (1982)

    Article  ADS  CAS  Google Scholar 

  25. Dieks, D.: Communication by EPR devices. Phys. Lett. A 92(6), 271–272 (1982)

    Article  ADS  Google Scholar 

  26. Yuen, H.P.: Amplification of quantum states and noiseless photon amplifiers[J]. Phys. Lett. A 113(8), 405–407 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  27. Pati, A.K., Braunstein, S.L.: Impossibility of deleting an unknown quantum state. Nature 404(6774), 164–165 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  28. Zurek, W.H.: Quantum cloning. Schrödinger’s sheep. Nature 404(6774), 130 (2000)

    Article  CAS  PubMed  Google Scholar 

  29. Bužek, V., Hillery, M., Werner, R.: Optimal manipulations with qubits: universal NOT gate. Phys. Rev. A 60, R2626 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  30. Gisin, N., Popescu, S.: Spin flips and quantum information for antiparallel spins. Phys. Rev. Lett. 83, 432 (1999)

    Article  ADS  CAS  Google Scholar 

  31. Jozsa, R.: A stronger no-cloning theorem. https://doi.org/10.48550/arXiv.quant-ph/0204153

  32. Pati, A.K.: Quantum cobwebs: Universal entangling of quantum states. Pramana 59(2), 221–228 (2002)

    Article  ADS  Google Scholar 

  33. Landauer, R.: Irreversibility and Heat Generation in the Computing Process. IBM J. Res. Develop. 5, 183 (1961)

    Article  MathSciNet  Google Scholar 

  34. Bennett, C.H.: The thermodynamics of computation-a review. Int. J. Theoret. Phys. 21, 905–940 (1982)

    Article  CAS  Google Scholar 

  35. Bužek, V., Hillery, M.: Quantum Copying: Beyond the No-Cloning Theorem. Phys. Rev. A 54(3), 1844 (1996)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  36. Hillery, M., Bužek, V.: Quantum copying: Fundamental inequalities. Phys. Rev. A 56, 1212–1216 (1997)

    Article  ADS  CAS  Google Scholar 

  37. Gisin, N., Massar, S.: Optimal quantum cloning machines. Phys. Rev. Lett. 79, 2153–2156 (1997)

    Article  ADS  CAS  Google Scholar 

  38. Bruß, D., Divincenzo, D. P., Ekert. A., et al.: Optimal universal and state-dependent quantum cloning. Phys. Rev. A 57(4), 2368–2378 (1998)

  39. Duan, L.M., Guo, G.C.: Probabilistic cloning and identification of linearly independent states. Phys. Rev. Lett. 80(22), 4999–5002 (1998)

    Article  ADS  CAS  Google Scholar 

  40. Murao, M., Jonathan, D., Plenio, M.B., et al.: Quantum telecloning and multiparticle entanglement. Phys. Rev. A 59(1), 156–161 (1999)

    Article  ADS  CAS  Google Scholar 

  41. Bruß, D., Cinchetti, M., Mauro, D.G., et al.: Phase covariant quantum cloning. Phys. Rev. A 62(1), 012302 (2000)

    Article  ADS  Google Scholar 

  42. Werner, R.: Optimal cloning of pure states. Phys. Rev. A 58, 1827–1832 (1998)

    Article  ADS  CAS  Google Scholar 

  43. Fan, H.: Quantum cloning of mixed states in symmetric subspace. Phys. Rev. A 68, 054301 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  44. Zou, X.B., Pahlke, K., Mathis, W.: Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED. Phys. Rev. A 67, 024304 (2003)

    Article  ADS  Google Scholar 

  45. Zhan, Y.B.: Assisted cloning of an unknown two-particle entangled state. Phys. Lett. A 336(4–5), 317–323 (2005)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  46. Ma, P.C., Zhan, Y.B.: Scheme for implementing assisted cloning of an unknown d-dimension equatorial quantum state by remote state preparation. Commun. Theor. Phys. 51, 57–59 (2009)

    Article  ADS  Google Scholar 

  47. Han, L.F., Yuan, H., Yang, M., et al.: Assisted cloning of anarbitrary unknown two-qubit state via a genuine four-qubit entangled state and positive operator-valued measure. Indian J. Pure Appl. Phys. 52, 563–570 (2014)

    Google Scholar 

  48. Hou, K., Shi, S.H.: Scheme for cloning an unknown entangled state with assistance via non-maximally entangled cluster states. Int. J. Theor. Phys. 48(1), 167–177 (2009)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  CAS  PubMed  Google Scholar 

  50. Zhan, Y.: A scheme for assisted cloning of a two-particle entangled state via GHZ class states. Chin. Opt. Lett. 3(101), S286–S289 (2005)

    ADS  Google Scholar 

  51. Ming, F., Yi, M.L., Jun, L., et al.: Assisted Cloning and Orthogonal Complementing of an Arbitrary Unknown Two-Qubit Entangled State. Commun. Theor. Phys. 46(5), 849–852 (2006)

    Article  ADS  Google Scholar 

  52. Zhang, J.Z., Xia, Y.: Use of two-particle entangled states to teleport unknown two-particle quantum state. Comput. Eng. Appl. 51(18), 82–85 (2015)

    CAS  Google Scholar 

  53. Han, L. F.: Theoretical study on quantum state teleportation, assisted cloning and reconstruction. Anhui University (2015)

  54. Araneda, G., Cisternas, N., Delgado, A.: Telecloning of qudits via partially entangled states. Quantum Inf. Process. 15, 3443–3458 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  55. Yu, Y., Zhao, N.: General quantum broadcast and multi-cast communicatioms based on entanglement. Optics. Express. 26(12), 29296 (2018)

    Article  ADS  PubMed  Google Scholar 

  56. Peng, J.Y., Yang, Z., Tang, L., et al.: Controlled quantum broadcast and multi-cast communications ofcomplex coefficient single-qubit states. Quantum Inf. Process. 21, 287 (2022)

    Article  ADS  Google Scholar 

  57. Yu, Y., Zha, X.W., Li, W.: Quantum broadcast scheme and multi-output quantum teleportation via four-qubit cluster state. Quantum. Inf. Process. 16(2), 41 (2017)

    Article  ADS  Google Scholar 

  58. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, New York (2000)

    Google Scholar 

  59. Bouwmeester, D., Pan, J.W., Mattle, K., et al.: Experimental quantum teleportation. Nature 390(390), 575 (1997)

    Article  ADS  CAS  Google Scholar 

  60. Deng, F.G., Li, X.H., Zhou, H.Y., et al.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72, 044302 (2005)

    Article  ADS  Google Scholar 

  61. Zhang, Z. J. , Yang, J. , Man, Z. X. , et al.: Multiparty secret sharing of quantum information using and identifying Bell states. Eur. Phys. J. D - Atomic, Molecular, Optical Plasma Phys. 33(1), 133–136 (2005)

  62. Yang, X. W., Chen, X.: Preparation of Bell states by dissipating quantum Zeno dynamics and Rydberg pump effect. Journal of Fujian Normal University: Natural Science Edition 37(1), 8(2021)

  63. Ding, D., Yan, F.L., Gao, T.: Entangler and analyzer for multiphoton Greenberger-Horne-Zeilinger states using weak nonlinearities. Sci. China Phys. Mechanics Astronomy 57(11), 2098–2103 (2014)

    Article  ADS  Google Scholar 

  64. Zeng, S., Nie, Y.Y.: Remote preparation scheme for 4-particle cluster states. Journal of Jiangxi Normal University: Natural Science Edition 39(1), 79–81 (2015)

    Google Scholar 

  65. Barrent, S.D., Kok, P., Nemoto, K.: Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities. Phys. Rev. A 71, 060302 (2005)

    Article  ADS  Google Scholar 

  66. Grice, W.P.: Arbitrarity complete Bell-state measurement using only linear optical ements. Phys. Rev. A 84(4), 5912–5916 (2011)

    Article  Google Scholar 

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Acknowledgements

This work is supported by Natural Science Foundation of China (No. 11071178, 11671284), Sichuan Province Education Department Scientific Research Innovation Team Foundation (No. 15TD0027), and Taizhou University high level talents research initiation fund (No. TZXY2017QDJJ011).

Funding

This work is supported by Natural Science Foundation of China (No. 11071178, 11671284), Sichuan Province Education Department Scientific Research Innovation Team Foundation (No. 15TD0027), and Taizhou University high level talents research initiation fund (No. TZXY2017QDJJ011).

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Authors and Affiliations

  1. School of Mathematic and Statistics, Kashi University, Kashi, Xinjiang, 844006, People’s Republic of China

    Jia-yin Peng & Jian-gang Tang

  2. School of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan, 641100, People’s Republic of China

    Jia-yin Peng

  3. College of Information Engineering, Taizhou University, Taizhou, Jiangsu, 225300, People’s Republic of China

    Hong-xuan Lei

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  1. Jia-yin Peng
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Correspondence to Hong-xuan Lei.

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Peng, Jy., Lei, Hx. & Tang, Jg. Multi-type-output Assisted Cloning of Unknown Single-qubit States. Int J Theor Phys 63, 7 (2024). https://doi.org/10.1007/s10773-023-05538-y

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