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Entanglement Protection about Four-Particle Cluster State

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Abstract

In the manuscript, we proposed three entanglement protection schemes with environment-assisted measurements and weak measurement reversals. The result demonstrates that the entanglement of four-particle cluster state is disturbed by the amplitude damping channel, but the weak measurement reversal operation helps to preserve the entanglement of the final output quantum state. In particular, the entanglement will reach the maximum if the weak measurement reversal strength is equal to the amplitude damping magnitude. Compared with the previous protection protocols, the performance of our schemes is more practical.

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References

  1. Zeng, G.H., Keitel, C.H.: Arbitrated quantum-signature scheme. Phys. Rev. A 65, 042312 (2002)

  2. Li, Q., Chan, W.H., Long, D.Y.: Arbitrated quantum signature scheme using Bell states. Phys. Rev. A 79, 054307 (2009)

  3. Wang, T.Y., Wei, Z.L.: One-time proxy signature based on quantum cryptography. Quantum Inf. Process. 11, 455 (2012)

  4. Amiri, R., Wallden, P., Kent, A., et al.: Secure quantum signatures using insecure quantum channels. Phys. Rev. A 93, 032325 (2016)

  5. Cai, X.Q., Wang, T.Y., Wei, C.Y., et al.: Cryptanalysis of multiparty quantum digital signatures. Quantum Inf. Process. 18, 252 (2019)

  6. Song, D., He, C., Cao, Z.W., et al.: Quantum teleportation of multiple qubits based on quantum Fourier transform. IEEE Communications Letters 22, 2427 (2018)

  7. Apollaro, T.J.G., Almeida, G.M.A., Lorenzo, S., et al.: Spin chains for two-qubit teleportation. Phys. Rev. A 100, 052308 (2019)

  8. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

  9. Harrow, A., Hayden, P., Leung, D.: Superdense coding of quantum states. Phys. Rev. Lett. 92, 187901 (2004)

  10. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)

  11. Wang, C., Deng, F.G., Li, Y.S., et al.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)

  12. Lin, S., Wen, Q.Y., Gao, F., et al.: Quantum secure direct communication with χ-type entangled states. Phys. Rev. A 78, 064304 (2008)

  13. Zhang, W., Ding, D.S., Sheng, Y.B., et al.: Quantum secure direct communication with 1uantum memory. Phys. Rev. Lett. 118, 220501 (2017)

  14. Gao, F., Liu, B., Wen, Q.Y., et al.: Flexible quantum private queries based on quantum key distribution. Opt. Exp. 20, 17411 (2012)

  15. Wei, C.Y., Cai, X.Q., Liu, B., et al.: A generic construction of quantum-oblivious-key-transfer-based private query with ideal database security and zero failure. IEEE Trans. Comput. 67 (1), 2-8 (2018)

  16. Biercuk, M.J., Usy, H., VanDevender, A.P., et al.: Experimental entanglement purification of arbitrary unknown states. Nature 458, 996 (2009)

  17. Khodjasteh, K., Lidar, D.A.: Fault-Tolerant Quantum Dynamical Decoupling. Phys. Rev. Lett. 95, 180501 (2005)

  18. Pryadko, L.P., Quiroz, G.: Soft-pulse dynamical decoupling with Markovian decoherence. Phys. Rev. A 80, 042317 (2009)

  19. Rungta, P., Bužek, V., Caves, C.M., et al.: Universal state inversion and concurrence in arbitrary dimensions. Phys. Rev. A 64, 042315 (2001)

  20. Viola, L., Knill, E., Lloyd, S.: Dynamical Decoupling of Open Quantum Systems. Phys. Rev. Lett. 82, 2417 (1999)

  21. Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098 (1996)

  22. Steane, A.M.: Error Correcting Codes in Quantum Theory. Phys. Rev. Lett. 77, 793 (1996)

  23. Knill, E., Laflamme, R.: Theory of quantum error-correcting codes. Phys. Rev. A 55, 900 (1997)

  24. Facchi, P., Lidar, D.A., Pascazio, S.: Unification of dynamical decoupling and the quantum Zeno effect. Phys. Rev. A 69, 032314 (2004)

  25. Itano, W.M., Heizen, D.J., Bollinger, J.J., Wineland, D.J.: Quantum Zeno effect. Phys. Rev. A 41, 2295 (1990)

  26. Wang, S.C., Li, Y., Wang, X.B., Kwek, L.C.: Operator Quantum Zeno Effect: Protecting Quantum Information with Noisy Two-Qubit Interactions. Phys. Rev. Lett. 110, 100505 (2013)

  27. Mabuchi, H., Zoller, P.: Inversion of quantum jump in quantum optical systems under continuous observation. Phys. Rev. Lett. 76, 3108 (1996)

  28. Sun, Q., Al-Amri, M., Zubairy, M.S.: Reversing the weak measurement of an arbitrary field with finite photon number. Phys. Rev. A 80, 033838 (2009)

  29. Man, Z.X., Xia, Y.J., An, N.B.: Manipulating entanglement of two qubits in a common environment by means of weak measurements and quantum measurement reversals. Phys. Rev. A 86, 012325 (2012)

  30. Aharonov, Y., Albert, D.Z, Vaidman, L.: How the result of a measurement of a component of the spin of a spin-\(\frac {1}{2}\) particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988)

  31. Korotkov, A.N., Keane, K.: Decoherence suppression by quantum measurement reversal. Phys. Rev. A 81, 040103 (2010)

  32. Kim, Y.S., Lee, J.C., Kwon, O., Kim, Y.H.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117 (2012)

  33. Xiao, X., Li, Y.L.: Protecting qutrit-qutrit entanglement by weak measurement and reversal. Eur. Phys. J. D. 67, 204 (2013)

  34. Liao, X.P., Fang, M.F., Fang, J.S., Zhu, Q.Q.: Preserving entanglement and the fidelity of three-qubit quantum states undergoing decoherence using weak measurement. Chin. Phys. B 23, 020304 (2014)

  35. Huang, J.: The protection of qudit states by weak measurement. Acta. Phys. Sin. 66, 010301 (2017)

  36. Wang, K., Zhao, X.Y., Yu, T.: Environment-assisted quantum state restoration via weak measurements. Phys. Rev. A 89, 042320 (2014)

  37. Xu, X.M., Cheng, L.Y., Liu, A.P., et al.: Environment-assisted entanglement restoration and improvement of the fidelity for quantum teleportation. Quantum Inf. Process. 14, 4147 (2015)

  38. Guan, S.Y., Jin, Z., Wu, H.J., et al.: Restoration of three-qubit entanglements and protection of tripartite quantum state sharing over noisy channels via environment-assisted measurement and reversal weak measurement. Quantum Inf. Process. 16, 137 (2017)

  39. Wu, H.J., Jin, Z., Zhu, A.D.: Protection of Telecloning Over Noisy Channels with Environment-Assisted Measurements and Weak Measurements. Int. J. Theor. Phys. 57, 1235 (2018)

  40. Dür, W., Briegel, H.J.: Stability of macroscopic entanglement under decoherence. Phys. Rev. Lett. 92, 180403 (2003)

  41. Dong, P., Xue, Z.Y., Yang, M., et al.: Generation of cluster states. Phys. Rev. A 73, 033818 (2006)

  42. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, London (2010)

  43. Aolita, L., Mintert, F.: Measuring Multipartite Concurrence with a Single Factorizable Observable. Phys. Rev. Lett. 97, 050501 (2006)

  44. Carvalho, A.R.R., Mintert, F., Buchleitner, A.: Decoherence and Multipartite Entanglement. Phys. Rev. Lett. 93, 230501 (2004)

  45. Briegal, H.J., Raussendorf, R.: Persistent Entanglement in Arrays of Interacting Particles. Phys. Rev. Lett. 86, 910 (2011)

  46. Li, D.C., Cao, Z.L.: Teleportation of Two-Particle Entangled State via Cluster State. Commun. Theor. Phys. 47, 464 (2007)

  47. Li, S.S., Nie, Y.Y., Hong, Z.H., et al.: Controlled Teleportation Using Four-Particle Cluster State. Commun. Theor. Phys. 50, 633 (2008)

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Acknowledgements

This work is supported by NSFC (Grant No. 11871019).

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Correspondence to Huijuan Zuo.

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Zuo, H., Li, Z. & Zang, Y. Entanglement Protection about Four-Particle Cluster State. Int J Theor Phys 60, 2193–2205 (2021). https://doi.org/10.1007/s10773-021-04836-7

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