Enhancing the fidelity of remote state preparation by partial measurements

  • Rui-Yuan Yang
  • Jin-Ming Liu


Enhancing the fidelity of quantum state transmission in noisy environments is a significant subject in the field of quantum communication. In this paper, improving the fidelity of a deterministic remote state preparation (RSP) protocol under decoherence is investigated with the technique of weak measurement (WM) and weak measurement reversal (WMR). We first construct the quantum circuit of the deterministic remote preparation of a single-qubit state through an EPR state with the assistance of an auxiliary qubit. Then, we analytically derive the average fidelity of the deterministic RSP protocol under the influence of generalized amplitude damping noises acting on the EPR state. Our results show that when only qubit 2 undergoes the decoherence channel, the average fidelity of the RSP protocol subject to generalized amplitude damping noise is the same as that subject to amplitude damping noise. Moreover, we analyze the optimal average fidelity of the above RSP process by introducing WM and WMR. It is found that the application of WM and a subsequent reversal operation could lead to the remarkable improvement of the average fidelity for most values of the decoherence parameters.


Remote state preparation Amplitude damping Average fidelity Weak measurement 



This work was supported by the National Natural Science Foundation of China under Grant No. 11174081, the Ministry of Science and Technology of China under Grant No. 2016YFB0501601, and the Natural Science Foundation of Shanghai under Grant No. 16ZR1448300.


  1. 1.
    Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557 (1992)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    Deng, F.G., Long, G.L., Liu, X.S.: A two-step quantum direct communication protocol using Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)ADSCrossRefGoogle Scholar
  6. 6.
    Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wooters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channel. Phys. Rev. Lett. 70, 1895 (1993)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Lo, H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    Bennett, C.H., Divincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wooters, W.K.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    Berry, D.W., Sanders, B.C.: Optimal remote state preparation. Phys. Rev. Lett. 90, 057901 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    Leung, D.W., Shor, P.W.: Oblivious remote state preparation. Phys. Rev. Lett. 90, 127905 (2003)ADSCrossRefGoogle Scholar
  12. 12.
    Xia, Y., Song, J., Song, H.S.: Remote preparation of the N-particle GHZ state using quantum statistics. Opt. Commun. 277, 219 (2007)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    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)ADSCrossRefGoogle Scholar
  14. 14.
    Liu, J.M., Feng, X.L., Oh, C.H.: Remote preparation of arbitrary two- and three-qubit states. EPL 87, 30006 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    Luo, M.X., Chen, X.B., Ma, S.Y., Yang, Y.X., Hu, Z.M.: Deterministic remote preparation of an arbitrary W-class state with multiparty. J. Phys. B At. Mol. Opt. Phy. 43, 065501 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    Xiao, X.Q., Liu, J.M., Zeng, G.H.: Joint remote state preparation of arbitrary two- and three-qubit states. J. Phys. B At. Mol. Opt. Phys. 44, 075501 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    An, N.B., Bich, C.T., Don, N.V., Kim, J.: Remote state preparation with unit success probability. Adv. Nat. Sci. Nanosci. Nanotechnol. 2, 035009 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    Chen, Q.Q., Xia, Y., Song, J.: Determinnistic joint remote preparation of an arbitrary three-qubit state via EPR pairs. J. Phys. A Math. Theor. 45, 055303 (2012)ADSzbMATHCrossRefGoogle Scholar
  19. 19.
    Dai, H.Y., Zhang, M., Zhang, Z.R., Xi, Z.R.: Probabilistic remote preparation of a four-particle entangled W state for the general case and for all kinds of the special cases. Commun. Theor. Phys. 60, 313 (2013)ADSzbMATHCrossRefGoogle Scholar
  20. 20.
    Giorgi, G.L.: Quantum discord and remote state preparation. Phys. Rev. A 88, 022315 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    An, N.B., Bich, C.T., Don, N.V.: Deterministic joint remote state preparation. Phys. Lett. A 375, 3570 (2011)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Zhan, Y.B., Ma, P.C.: Deterministic joint remote preparation of arbitrary two- and three-qubit entangled states. Quantum Inf. Process. 12, 997 (2013)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Jiang, M., Jiang, F.: Deterministic joint remote preparation of arbitrary multi-qudit states. Phys. Lett. A 377, 2524 (2013)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Wang, D., Huang, A.J., Sun, W.Y., Shi, J.D., Ye, L.: Practical single-photon-assisted remote state preparation with non-maximally entanglement. Quantum Inf. Process. 15, 3367–3381 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Wang, D., Hoehn, R.D., Ye, L., Kais, S.: Generalized remote preparation of arbitrary m-qubit entangled states via genuine entanglements. Entropy 17, 1755–1774 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    Znidaric, M.: Dissipative remote-state preparation in an interacting medium. Phys. Rev. Lett. 116, 030403 (2016)ADSzbMATHCrossRefGoogle Scholar
  27. 27.
    He, Y.H., Lu, Q.C., Liao, Y.M., Qin, X.C., Qin, J.S., Zhou, P.: Bidirectional controlled remote implementation of an arbitrary single qubit unitary operation with EPR and cluster states. Int. J. Theor. Phys. 54, 1726 (2015)zbMATHCrossRefGoogle Scholar
  28. 28.
    Liao, Y.M., Zhou, P., Qin, X.C., He, Y.H., Qin, J.S.: Controlled remote preparing of an arbitrary 2-qudit state with two-particle entanglements and positive operator-valued measure. Commun. Theor. Phys. 61, 315–321 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Peters, N.A., Barreiro, J.T., Goggin, M.E., Wei, T.C., Kwiat, P.G.: Remote state preparation: arbitrary remote control of photon polarization. Phys. Rev. Lett. 94, 150502 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    Rosenfeld, W., Berner, S., Volz, J., Weber, M., Weinfurter, H.: Remote preparation of an atomic quantum memory. Phys. Rev. Lett. 98, 050504 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    Liu, W.T., Wu, W., Ou, B.Q., Chen, P.X., Li, C.Z., Yuan, J.M.: Experimental remote preparation of arbitrary photon polarization states. Phys. Rev. A 76, 022308 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    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)ADSCrossRefGoogle Scholar
  33. 33.
    Radmark, M., Wiesniak, M., Zukowski, M., Bourennane, M.: Experimental multilocation remote state preparation. Phys. Rev. A 88, 032304 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    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 306, 271 (2003)ADSCrossRefGoogle Scholar
  35. 35.
    Yu, T., Eberly, J.H.: Finite-time disentanglement via spontaneous emission. Phys. Rev. Lett. 93, 140404 (2004)ADSCrossRefGoogle Scholar
  36. 36.
    Almeida, M.P., de Melo, F., Hor-Meyll, M., Salles, A., Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L.: Environment-induced sudden death of entanglement. Science 316, 579–582 (2007)ADSCrossRefGoogle Scholar
  37. 37.
    Liang, H.Q., Liu, J.M., Feng, S.S., Chen, J.G.: Remote state preparation via a GHZ-class state in noisy environments. J. Phys. B At. Mol. Opt. Phys. 44, 115506 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    Sharma, V., Shukla, C., Banerjee, S., Pathak, A.: Controlled bidirectional remote state preparation in noisy environment: a generalized view. Quantum Inf. Process. 14, 3441–3464 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  39. 39.
    Li, J.F., Liu, J.M., Xu, X.Y.: Deterministic joint remote preparation of an arbitrary two-qubit state in noisy environments. Quantum Inf. Process. 14, 3465–3481 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Falaye, B.J., Sun, G.H., Camacho-Nieto, O., Dong, S.H.: JRSP of three-particle state via three tripartite GHZ class in quantum noisy channels. Int. J. Quantum Inf. 14, 1650034 (2016)zbMATHCrossRefGoogle Scholar
  41. 41.
    Xiang, G.Y., Li, J., Yu, B., Guo, G.C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2005)ADSCrossRefGoogle Scholar
  42. 42.
    Sun, Q.Q., Amri, M.A., Zubairy, M.S.: Reversing the weak measurement of an arbitrary field with finite photon number. Phys. Rev. A 80, 033838 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    Man, Z.X., Xia, Y.J.: Manipulating entanglement of two qubits in a common environment by means of weak measurements and quantum measurement reversals. Phys. Rev. A 86, 012325 (2012)ADSCrossRefGoogle Scholar
  44. 44.
    Wang, S.C., Yu, Z.W., Zou, W.J., Wang, X.B.: Protecting quantum states from decoherence of finite temperature using weak measurement. Phys. Rev. A 89, 022318 (2014)ADSCrossRefGoogle Scholar
  45. 45.
    Zong, X.L., Du, C.Q., Yang, M., Yang, Q., Cao, Z.L.: Protecting remote bipartite entanglement against amplitude damplitude damping by local unitary operations. Phys. Rev. A 90, 062345 (2014)ADSCrossRefGoogle Scholar
  46. 46.
    Guo, J.L., Wei, J.L.: Dynamics and protection of tripartite quantum correlations in a thermal bath. Ann. Phys. 354, 522–533 (2015)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Katz, N., Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., O’Connell, A., Wang, H., Cleland, A.N., Martinis, J.M., Korotkov, A.N.: Reversal of the weak measurement of a quantum state in a superconducting phase qubit. Phys. Rev. Lett. 101, 200401 (2008)ADSCrossRefGoogle Scholar
  48. 48.
    Lee, J.C., Jeong, Y.C., Kim, Y.S., Kim, Y.H.: Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19, 16309 (2011)ADSCrossRefGoogle Scholar
  49. 49.
    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)CrossRefGoogle Scholar
  50. 50.
    Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988)ADSCrossRefGoogle Scholar
  51. 51.
    Brańczyk, A.M., Mendonca, P.E.M.F., Gilchrist, A., Doherty, A.C., Bartlett, S.D.: Quantum control of a single qubit. Phys. Rev. A 75, 012329 (2007)ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    Xiao, X., Li, Y.L.: Protecting qutrit-qutrit entanglement by weak measurement and reversal. Eur. Phys. J. D 67, 204 (2013)ADSCrossRefGoogle Scholar
  53. 53.
    Paraoanu, G.S.: Generalized partial measurements. EPL 93, 64002 (2011)ADSCrossRefGoogle Scholar
  54. 54.
    Korotkov, A.N., Keane, K.: Decoherence suppression by quantum measurement reversal. Phys. Rev. A 81, 040103(R) (2010)ADSCrossRefGoogle Scholar
  55. 55.
    Cheong, Y.W., Lee, S.W.: Balance between information gain and reversibility in weak measurement. Phys. Rev. Lett. 109, 150402 (2012)ADSCrossRefGoogle Scholar
  56. 56.
    Wang, Q., He, Z., Yao, C.M.: Decoherence suppression of a qutrit system with both spontaneous emission and dephasing by weak measurement and reversal. Phys. Scr. 90, 055102 (2015)ADSCrossRefGoogle Scholar
  57. 57.
    Doustimotlagh, N., Wang, S.H., You, C.L., Long, G.L.: Enhancement of quantum correlations between two particles under decoherence in finite-temperature environment. EPL 106, 60003 (2014)ADSCrossRefGoogle Scholar
  58. 58.
    Guo, J.L., Wei, J.L., Qin, W.: Enhancement of quantum correlations in qubit-qutrit system under decoherence of finite temperature. Quantum Inf. Process. 14, 1399–1410 (2015)ADSzbMATHCrossRefGoogle Scholar
  59. 59.
    Shi, J.D., Wang, D., Ma, W.C., Ye, L.: Enhancing quantum correlation in open-system dynamics by reliable quantum operations. Quantum Inf. Process. 14, 3569–3579 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Song, W., Yang, M., Cao, Z.L.: Purifying entanglement of noisy two-qubit states via entanglement swapping. Phys. Rev. A 89, 014303 (2014)ADSCrossRefGoogle Scholar
  61. 61.
    Shi, J.D., Xu, S., Ma, W.C., Song, X.K., Ye, L.: Purifying two-qubit entanglement in nonidentical decoherence by employing weak measurements. Quantum Inf. Process. 14, 1387–1397 (2015)ADSzbMATHCrossRefGoogle Scholar
  62. 62.
    Liao, X.P., Ding, X.Z., Fang, M.F.: Improving the payoffs of cooperators in three-player cooperative game using weak measurements. Quantum Inf. Process. 14, 4395–4412 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  63. 63.
    Pramanik, T., Majumdar, A.S.: Improving the fidelity of teleportation through noisy channels using weak measurement. Phys. Lett. A 377, 3209–3215 (2013)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  64. 64.
    Qiu, L., Tang, G., Yang, X.Q., Wang, A.M.: Enhancing teleportation fidelity by means of weak measurements or reversal. Ann. Phys. 350, 137–145 (2014)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  65. 65.
    Xu, X.M., Cheng, L.Y., Liu, A.P., Su, S.L., Wang, H.F., Zhang, S.: Environment-assisted entanglement restoration and improvement of the fidelity for quantum teleportation. Quantum Inf. Process. 14, 4147–4162 (2015)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  66. 66.
    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)ADSCrossRefGoogle Scholar
  67. 67.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  68. 68.
    Oh, S., Lee, S., Lee, H.W.: Fidelity of quantum teleportation through noisy channels. Phys. Rev. A 66, 022316 (2002)ADSMathSciNetCrossRefGoogle Scholar
  69. 69.
    Kim, Y.S., Cho, Y.W., Ra, Y.S., Kim, Y.H.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978 (2009)ADSCrossRefGoogle Scholar

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Precision Spectroscopy, Department of PhysicsEast China Normal UniversityShanghaiChina

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