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量子隐形传态保真度的新公式及应用

贾芳 刘寸金 胡银泉 范洪义

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量子隐形传态保真度的新公式及应用

贾芳, 刘寸金, 胡银泉, 范洪义

New formula for calculating the fidelity of teleportation and its applications

Jia Fang, Liu Cun-Jin, Hu Yin-Quan, Fan Hong-Yi
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  • 基于传统的Kimble-Braunstein量子隐形传态方案,利用纠缠态表象方法导出了平均意义下输出量子态的密度算符表示输出态算符与输入态、纠缠源的特征函数的关系,以及输出态特征函数与以上特征函数的简洁关系.基于此,对于任意的双模纠缠源,进一步推导了传输相干态的保真度公式它仅仅表示成纠缠源的Q函数的一个简洁积分.这为保真度计算提供了一条方便有效的途径.作为应用,我们考察了包括高斯与非高斯纠缠态作为纠缠源实现相干态传输的保真度.
    Quantum teleportation plays an important role in quantum information science. In order to obtain the effect of quantum teleportation of a quantum state by using an entangled resource, the fidelity of teleporting the quantum state should be calculated. Braunstein and Kimble[Phys. Rev. Lett. 80 869 (1998)] derived a formula of calculating the fidelity of quantum teleportation for Gaussian entangled resource and any input state to be teleported. Then, the point is how to calculate the quantum teleportation fidelity for any entangled resource. In this paper, werealize this purpose by using the entangled state representation. First, we derive the Weyl expansion of any density operator by using the completeness relation between coherent state and P-representation. Then using the orthogonal property of entangled state representation and the traditional Kimble-Braunstein scheme of quantum teleportation, we further derive the mean density operator of the output state, which means that we establish the relation between the output density operator and the characteristic functions of the input state to be teleported and the entangled resources. The characteristic function of the output state is also derived which is in the concise form relating these two characteristic functions above. Then we further obtain a new formula for calculating the quantum teleportation fidelity for the coherent state input and any two-mode entangled resource. It is shown that the fidelity of teleportation can be easily calculated when the Q-function of the normally ordering form of entangled resource is known. This is a convenient way of obtaining the fidelity of teleportation. As its applications, some Gaussian and non-Gaussian entangled states are examined to teleport the coherent state, whose results are correct.
      通信作者: 贾芳, jenshier@126.com
    • 基金项目: 国家自然科学基金(批准号:11664017,11264018,11464018)、江西省自然科学基金(批准号:20151BAB212006)、江西省学位与研究生教育教学改革研究项目(批准号:JXYJG-2013-027)和江西省教育厅科技项目(批准号:GJJ14274,GJJ14276)资助的课题.
      Corresponding author: Jia Fang, jenshier@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11664017, 11264018, 11464018), the Natural Science Foundation of Jiangxi Province of China (Grant No. 20151BAB212006), the Academic Degree and Postgraduate Education Foundation of Jiangxi Province of China (Grant No. JXYJG-2013-027), and the Education Department of Jiangxi Province of China (Grant Nos. GJJ14274, GJJ14276).
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  • [1]

    Bouwmeester D, Ekert A K, Zeilinger A 2000The Physics of Quantum Information (Berlin:Springer)

    [2]

    Cochrane P T, Ralph T C, Mibum G J 2002Phys. Rev. A 65 062306

    [3]

    Cochrane P T, Ralph T C 2003Phys. Rev. A 67 22313

    [4]

    Parigi V, Zavatta A, Kim M S, Bellini M 2007Science 317 1890

    [5]

    Hu L Y, Zhang Z M 2012J. Opt. Soc. Am. B 29 529

    [6]

    Hu L Y, Jia F, Zhang Z M 2012J. Opt. Soc. Am. B 29 1456

    [7]

    Hu L Y, Zhang Z M 2013J. Opt. Soc. Am. B 30 518

    [8]

    Wang S, Hou L L, Chen X F, Xu X F 2015Phys. Rev. A 91 063832

    [9]

    Zhang H L, Hu Y Q, Jia F, Hu L Y 2014Int. J. Theor. Phys. 53 2091

    [10]

    Braunstein S L, Kimble H J 1998Phys. Rev. Lett. 80 869

    [11]

    Hu L Y, Liao Z Y, Ma S L, Zubairy M S 2016Phys. Rev. A 93 033807

    [12]

    Scully M O, Zubairy M S 1997Quantum Optics (Cambridge:Cambridge University Press)

    [13]

    Fan H Y 2002Phys. Lett. A 294 253

    [14]

    Jia F, Xu X X, Liu C J, Huang J H, Hu L Y, Fan H Y 2014Acta Phys. Sin. 63 220301(in Chinese)[贾芳, 徐学翔, 刘寸金, 黄接辉, 胡利云, 范洪义2014物理学报63 220301]

    [15]

    Fan H Y 1997Representation and Transformation Theory in Quantum Mechanics (Shanghai:Shanghai Scientific and Technical Publisher) (in Chinese) p27[范洪义1997量子力学表象与变换论——狄拉克符号法进展(上海:上海科技出版社) p27]

    [16]

    Marian P, Marian T A 2006Phys. Rev. A 74 042306

    [17]

    Puri R R 2001Mathematical Methods of Quantum Optics (Berlin:Springer-Verlag) (Appendix A)

    [18]

    Hu L Y, Fan H Y, Zhang Z M 2013Chin. Phys. B 22 034202

    [19]

    Xu X X, Hu L Y, Fan H Y 2009Mod. Phys. Lett. A 24 2623

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出版历程
  • 收稿日期:  2016-04-14
  • 修回日期:  2016-08-10
  • 刊出日期:  2016-11-05

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