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Effective deterministic joint remote preparation of the Knill–Laflamme–Milburn state in collective noise environment

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Abstract

We present a scheme for implementing deterministic joint remote preparation of the Knill–Laflamme–Milburn state with two GHZ states as the quantum channel. Assuming that four of the six involved qubits collectively suffer the same type of noise, we first investigate the effects of four typical types of noises on the protocol by means of Kraus operators. It is shown that the bit-flip and amplitude damping noise are the severe noises for decoherence rate \(\chi <0.5\), followed by the depolarizing and phase-flip channel, respectively. Interestingly, the efficiency of the scheme can be restored by adding decoherence when \(\chi >0.5\) in bit-flip and phase-flip noise channel. Afterward, we investigate the dynamics of deterministic joint remote state preparation for dissipative environments. Analytical and numerical calculations show that the quality of our scheme can be enhanced by adjusting the system detuning no matter whether the non-Markovian effect is applicable or not.

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References

  1. Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  2. Lo, H.K.: Classical-communication cost indistributed quantum information processing: a generalization of quantum communication complexity. Phys. Rev. A 62(1), 012313 (2000)

    ADS  Google Scholar 

  3. 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 

  4. Pati, A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63(1), 014302 (2001)

    ADS  Google Scholar 

  5. Shi, B.S., Tomita, T.: Remote state preparation of an entangled state. J. Opt. B Quantum Semiclass. Opt. 4, 380 (2002)

    ADS  MathSciNet  Google Scholar 

  6. Leung, D., Shor, P.W.: Oblivious remote state preparation. Phys. Rev. Lett. 90, 197901 (2003)

    Google Scholar 

  7. Berry, D.W., Sanders, B.C.: Optimal remote state preparation. Phys. Rev. Lett. 90(5), 057901 (2003)

    ADS  Google Scholar 

  8. 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(2), 22310 (2004)

    ADS  Google Scholar 

  9. Peters, N.A., Barreiro, J.T., Goggin, M.E., Wei, T., Kwiat, P.G.: Remote state preparation: arbitrary remote control of photon polarization. Phys. Rev. Lett. 94(15), 150502 (2005)

    ADS  Google Scholar 

  10. Dai, H., Chen, P., Liang, L., Li, C.: Classical communication cost and remote preparation of the four-particle GHZ class state. Phys. Lett. A 355(4), 285–288 (2006)

    ADS  Google Scholar 

  11. Liu, J.M., Feng, X.L., Oh, C.H.: Remote preparation of arbitrary two- and three-qubit states. EPL 87(3), 30006 (2009)

    ADS  Google Scholar 

  12. Luo, M.X., Chen, X.B., Yang, Y.X., Niu, X.X.: Experimental architecture of joint remote state preparation. Quantum Inf. Process. 11(3), 751–767 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Wang, D., Hu, Y.D., Wang, Z.Q., Ye, L.: Efficient and faithful remote preparation of arbitrary three- and four-particle W-class entangled states. Quantum Inf. Process. 14(6), 2135–2151 (2015)

    ADS  MATH  Google Scholar 

  14. Chen, X.B., Sun, Y.R., Xu, G., Jia, H.Y., Qu, Z., Yang, Y.X.: Controlled bidirectional remote preparation of three-qubit state. Quantum Inf. Process. 16(10), 244 (2017)

    ADS  MATH  Google Scholar 

  15. Le, J.H., Cavailles, A., Raskop, J., Huang, K., Laurat, J.: Remote preparation of continuous-variable qubits using loss-tolerant hybrid entanglement of light. Optica 5(8), 1012 (2018)

    ADS  Google Scholar 

  16. Li, Y.H., Qiao, Y., Sang, M.H., Nie, Y.Y.: Bidirectional controlled remote state preparation of an arbitrary two-qubit state. Internat. J. Theoret. Phys. 58(7), 2228 (2019)

    MATH  Google Scholar 

  17. Nikaeen, M., Ramezani, M., Bahrampour, A.: Optimal exploitation of resource in remote state preparation. Phys. Rev. A 102, 012416 (2020)

    ADS  MathSciNet  Google Scholar 

  18. Wei, D.X., Luo, J., Yang, X.D.: Experimental realization of information transmission between not-directly-coupled spins on NMR quantum computers. Chin. Phys. 13, 817 (2004)

    Google Scholar 

  19. Liu, W.T., et al.: Experimental remote preparation of arbitrary photon polarization states. Phys. Rev. A 76, 022308 (2007)

    ADS  Google Scholar 

  20. 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 

  21. Dakic, B., et al.: Quantum discord as resource for remote state preparation. Nat. Phys 8(9), 666 (2012)

    Google Scholar 

  22. Xiang, G.Y., Li, J., Yu, B., Guo, G.C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2015)

    ADS  Google Scholar 

  23. Jiang, Y.F., et al.: Remote blind state preparation with weak coherent pulses in the field. Phys. Rev. Lett. 123(10), 100503 (2019)

    ADS  Google Scholar 

  24. An, N.B., Bich, C.T., Don, N.V.: Deterministic joint remote state preparation. Phys. Lett. A 375(41), 3570–3573 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  25. Zhan, Y.B., Ma, P.C.: Deterministic joint remote preparation of arbitrary two- and three-qubit entangled states. Quantum Inf. Process. 12(2), 997–1009 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  26. Xia, Y., Song, J., Song, H.S.: Multiparty remote state preparation. J. Phys. B At. Mol. Opt. Phys. 40(18), 3719 (2007)

    ADS  Google Scholar 

  27. An, N.B., Kim, J.: Joint remote state preparation. J. Phys. B At. Mol. Opt. Phys. 41(9), 095501 (2008)

    ADS  Google Scholar 

  28. Wu, W., Liu, W.T., Chen, P.X., Li, C.Z.: Deterministic remote preparation of pure and mixed polarization states. Phys. Rev. A 81(4), 042301 (2010)

    ADS  Google Scholar 

  29. Zhan, Y.B., Ma, P.C.: Deterministic remote preparation of arbitrary two- and three-qubit states. EPL 98(4), 40005 (2012)

    ADS  Google Scholar 

  30. Wang, Y., Ji, W.: Deterministic joint remote state preparation of arbitrary two- and three-qubit states. Chin. Phys. B 22(2), 020306 (2013)

    ADS  Google Scholar 

  31. Chen, Q.Q., Xia, Y., Song, J.: Deterministic joint remote preparation of an arbitrary three-qubit state via EPR pairs. J. Phys. A Math. Theor. 45(5), 055303 (2012)

    ADS  MathSciNet  MATH  Google Scholar 

  32. Ma, P.C., Chen, G.B., Zhan, Y.B.: Schemes for deterministic joint remote preparation of an arbitrary tripartite four-qubit entangled state. Laser Phys. 26(10), 105201 (2016)

    ADS  Google Scholar 

  33. Bich, C.T., et al.: Deterministic joint remote preparation of an equatorial hybrid state via high-dimensional Einstein–Podolsky–Rosen pairs: active versus passive receiver. Quantum Inf. Process. 17(4), 1–12 (2018)

    MathSciNet  MATH  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  35. Wang, M.M., Qu, Z.G.: Effect of quantum noise on deterministic joint remote state preparation of a qubit state via a GHZ channel. Quantum Inf. Process. 15(11), 4805 (2016)

    ADS  MATH  Google Scholar 

  36. Qian, Y.J., Xue, S.B., Jiang, M.: Deterministic remote preparation of arbitrary single-qubit state via one intermediate node in noisy environment. Phys. Lett. A 384, 126204 (2020)

    MATH  Google Scholar 

  37. Guan, X.W., Chen, X.B., Wang, L.C., Yang, Y.X.: Joint remote preparation of an arbitrary two-qubit state in noisy environments. Int. J. Theor. Phys. 53(7), 2236 (2014)

    MATH  Google Scholar 

  38. 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(6), 581 (2017)

    ADS  Google Scholar 

  39. Wang, M.M., Qiu, Z.G., Wang, W., Chen, J.G.: Effect of noise on deterministic joint remote preparation of an arbitrary two-qubit state. Quantum Inf. Process. 16, 140 (2017)

    ADS  MATH  Google Scholar 

  40. Dash, T., Sk, R., Panigrahi, P.K.: Deterministic joint remote state preparation of arbitrary two-qubit state through noisy cluster-GHZ channel. Opt. Commun. 464, 125518 (2020)

    Google Scholar 

  41. Zhang, Z.H., Zhao, C.R., Wang, J.W., Shu, L.: Joint remote state preparation of mixed states. J. Phys. B At. Mol. Opt. Phys. 53(2), 025501 (2020)

    ADS  Google Scholar 

  42. Nguyen, V.H., Cao, T.B., Nguyen, B.A.: Optimal joint remote state preparation in the presence of various types of noises. Adv. Nat. Sci.: Nanosci. Nanotechnol. 8, 015012 (2017)

  43. Chen, Z.F., Liu, J.M., Ma, L.: Deterministic joint remote preparation of an arbitrary two-qubit state in the presence of noise. Chin. Phys. B 23(2), 020312 (2014)

    ADS  Google Scholar 

  44. Zhang, Z.H., Sun, M.: Enhanced deterministic joint remote state preparation under Pauli channels with memory. Phys. Scr. 95(5), 055107 (2020)

    ADS  Google Scholar 

  45. Li, J.F., Liu, J.M., Feng, X.L., Oh, C.H.: Deterministic remote two-qubit state preparation in dissipative environments. Quantum Inf. Process. 15(5), 2155–2168 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  46. Knill, E., Laflamme, R., Milburn, G.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)

    ADS  Google Scholar 

  47. Modlawska, J., Grudka, A.: Adaptive quantum teleportation. Phys. Rev. A 79, 064302 (2009)

    ADS  MathSciNet  Google Scholar 

  48. Franson, J.D., Donegan, M.M., Fitch, M.J., Jacobs, B.C., Pittman, T.B.: High-fidelity quantum logic operations using linear optical elements. Phys. Rev. Lett. 89, 137901 (2002)

    ADS  Google Scholar 

  49. Lemr, K., Fiurášek, J.: Preparation of states of two photons in several spatial modes. Phys. Rev. A 77, 023802 (2008)

    ADS  Google Scholar 

  50. Cheng, L.Y., Wang, H.F., Zhang, S., Yeon, K.H.: Generation of two-atom knill-laflamme-milburn states with cavity quantum electrodynamics. J. Opt. Soc. Am. B 29, 1584–1588 (2012)

    ADS  Google Scholar 

  51. Li, D.X., et al.: Engineering steady Knill-Laflamme-Milburn state of Rydberg atoms by dissipation. Opt. Express 26(3), 2292 (2018)

    ADS  Google Scholar 

  52. Fortes, R., Rigolin, G.: Fighting noise with noise in realistic quantum teleportation. Phys. Rev. A 92, 012338 (2015)

    ADS  Google Scholar 

  53. Badziag, P., Horodecki, M., Horodecki, P., Horodecki, R.: Local environment can enhance fidelity of quantum teleportation. Phys. Rev. A 62, 012311 (2000)

    ADS  Google Scholar 

  54. Breuer, H.P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  55. Garraway, B.M.: Nonperturbative decay of an atomic system in a cavity. Phys. Rev. A 55, 2290 (1997)

    ADS  Google Scholar 

  56. Bellomo, B., Franco, R.L., Compagno, G.: Non-Markovian effects on the dynamics of entanglement. Phys. Rev. Lett. 99, 160502 (2007)

    ADS  Google Scholar 

  57. Vacchini, B., Breuer, H.P.: Exact master equations for the non-Markovian decay of a qubit. Phys. Rev. A 81, 042103 (2010)

    ADS  Google Scholar 

  58. Xiao, X., Fang, M.F., Li, Y.L.: Wu, Chao: Robust entanglement preserving by detuning in non-Markovian regime. J. Phys. B: At. Mol. Opt. Phys. 42, 235502 (2009)

    ADS  Google Scholar 

  59. Zhang, Y.L., Zhou, Q.P., Kang, G.D., Zhou, F., Wang, X.B.: Remote state preparation in non-Markovian environment. Int. J. Quantum Inf. 10, 1250030 (2012)

    MATH  Google Scholar 

  60. Xu, Z.Y., Liu, C., Luo, S., Zhu, S.: Non-Markovian effect on remote state preparation. Ann. Phys. 356, 29–36 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  61. Chruscinski, D., Kossakowski, A.: arXiv:1006.2764

  62. Dijkstra, A.G., Tanimura, Y.: Non-Markovian entanglement dynamics in the presence of system-bath coherence. Phys. Rev. Lett. 104, 250401 (2010)

    ADS  Google Scholar 

  63. Breuer, H.P., Laine, E.M., Piilo, J., Vacchini, B.: Colloquium: Non-Markovian dynamics in open quantum systems. Rev. Mod. Phys 88, 021002 (2006)

    ADS  Google Scholar 

  64. Rajagopal, A.K., Usha Devi, A.R., Rendell, R.W.: Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian forms. Phys. Rev. A 82, 042107 (2010)

    ADS  Google Scholar 

  65. Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41, 2315 (1994)

    ADS  MathSciNet  MATH  Google Scholar 

  66. Rivas, A., Huelga, S.F., Plenio, S.F.: Entanglement and non-Markovianity of quantum evolutions. Phys. Rev. Lett. 105, 050403 (2010)

    ADS  MathSciNet  Google Scholar 

  67. Zou, W.J., et al.: Protecting entanglement from finite-temperature thermal noise via weak measurement and quantum measurement reversal. Phys. Rev. A 95, 042342 (2017)

    ADS  Google Scholar 

  68. Liu, B.H., et al.: Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems. Nat. Phys. 7, 931 (2011)

    Google Scholar 

  69. Smirne, A., Brivio, D., Cialdi, S., Vacchini, B., Paris, M.G.A.: Experimental investigation of initial system-environment correlations via trace-distance evolution Phys. Rev. A 84, 032112 (2011)

    Google Scholar 

  70. Gessner, M., et al.: Local detection of quantum correlations with a single trapped ion. Nat. Phys. 10, 105 (2014)

    Google Scholar 

  71. Liu, J., Lu, X.M., Wang, X.G.: Nonunital non-Markovianity of quantum dynamics. Phys. Rev. A 87, 042103 (2013)

    ADS  Google Scholar 

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Acknowledgements

K. Hou and M. Shi thank the support the National Natural Science Foundation of China (Grant No. 11805004) and the Doctor Foundation of Anhui Jianzhu University(Grant No. 2020QDZ21). Z.Y. Chen thanks the support of the Higher Education Quality Engineering Project of Anhui Jianzhu University (Grant No. 2020XSXX01). X.Y.Zhang thanks the support of the Natural Science Fundation of Education Department of Anhui Province (Grant No. KJ2020A0484).

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Authors and Affiliations

  1. Department of Mathematics and Physics, Anhui JianZhu University, Hefei, 230601, China

    Kui Hou, Zun-Yi Chen, Min Shi & Xue-Yong Zhang

  2. Key Laboratory of Architectural Acoustics Environment of Anhui High Education Institutes, Hefei, 230601, China

    Kui Hou & Xue-Yong Zhang

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  1. Kui Hou
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Hou, K., Chen, ZY., Shi, M. et al. Effective deterministic joint remote preparation of the Knill–Laflamme–Milburn state in collective noise environment. Quantum Inf Process 20, 225 (2021). https://doi.org/10.1007/s11128-021-03163-4

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