自由空间量子通信中偏振光子传输和操控的理论与模拟研究
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摘要
传统密码技术是建立在数学算法复杂度基础上的,随着量子计算机的发展,传统密码在原理上都可以被破译,通信安全隐患十分突出。基于量子力学基本原理的量子密码在原理上是“无法破译”、“绝对安全”的,故而量子密码可以实现真正意义上的保密通信,是国家安全和未来信息技术发展的重要研究领域。
由于自由空间量子密钥传输对将来利用卫星进行量子密钥分配并进而建立全球量子保密通信网具有重大意义,所以在自由空间进行量子密钥分配引起了人们的广泛关注和深入研究。本论文研究自由空间量子通信的相关理论问题,建立光子大气传输的适当的理论模型,分析光子偏振态如何受大气散射的影响,提出偏振光子纠缠浓缩的实现方案。本论文的完成将为自由空间量子通信的实施提供必要的理论支持和有价值的技术方案,这对于最终实现基于卫星的全球量子通信具有一定的理论意义和实用价值。论文主要研究成果有：
从Maxwell方程出发比较分析了Rayleigh近似与Mie散射的散射振幅与散射截面,得到当散射粒子的尺度参数较小时,Rayleigh散射与Mie散射符合的很好,可用Rayleigh散射代替Mie散射。同时比较分析了Born近似和Mie散射的散射振幅与散射截面,计算表明相对折射率在[1.01,1.09]之间的散射粒子,其尺度参数满足特定条件时可用Born散射代替Mie散射。这样,在满足条件的散射理论计算中,可避免繁琐的无穷级数计算。
针对自由空间量子通信,给出了前向直向散射的简化处理方案,推导了偏振光子Mie散射前向有效Mueller矩阵及各矩阵元之间的关系。
用矢量Monte Carlo方法模拟均匀大气中偏振光子的多次散射过程,得到表征大气信道特征的Mueller矩阵模拟图,并以此分析讨论了气溶胶粒子尺度对光子偏振态的影响。当粒子尺度较小时,光子的退偏效应很明显,光子偏振度对粒子尺度的变化非常敏感；当粒子尺度较大时,光子的偏振度较大,退偏效应弱,偏振度对粒子尺度的变化不敏感。
利用偏振光子的多次散射模型和经过改进的多层大气散射模型,研究了量子通信中光子与大气的相互作用过程,分析了单光子密钥分配过程中大气散射对偏振态的影响。结果表明,光子上行时偏振态保持的效果明显比下行时要好；光子在传输相同距离的情况下,高海拔位置比低海拔位置偏振态的变化幅度要小。
针对偏振纠缠光子在量子通信中由于偏振态变化而引起的纠缠度下降问题,提出了一种线性光学系统的理论方案,通信双方利用该系统可以确定性地从两对部分纠缠光子中提取出一对最大纠缠光子。这套装置借助于将两光子偏振态分别隐形传送到第三个光子的路径和偏振态上,通过实现单光子偏振态和路径态的操作,来完成两光子偏振态的操控,进而克服了光子间弱耦合带来的困难。
Traditional cryptography is based on complicated mathematical algorithms. However, with the development of quantum computers, the traditional cryptography could be deciphered, so communications security constitutes a conspicuous problem. Based on basic principles of quantum mechanics, quantum cryptography is "can not decipher" and "absolute security", therefore quantum cryptography can achieve a real sense of secure communications and an important research field of national security as well as the bright future for the development of information technology.
Because free-space quantum key transmission is of great significance to future quantum key distribution using satellites as well as to establishing a global network of quantum secure communication, free-space quantum key distribution has aroused widespread concern. This thesis studies the theory of free-space quantum communication and establishes the appropriate theoretical model of photon propagation in the atmosphere, analyzes the photon polarization vector by the atmospheric scattering effects. The completion of this thesis will provide necessary theoretical support and valuable technical program for free-space quantum communication, which will be of great importance for the eventual realization of satellite-based global quantum communication. Main conclusions of this thesis include:
We have analyzed and compared Rayleigh scattering and Mie scattering. It is shown that Rayleigh scattering and Mie scattering are in good agreement when the scale parameter is small. But when the scale parameter is large, dependence of Mie scattering intensity on wavelength is not obvious. We have analyzed and compared of Born approximation and Mie scattering of spherical particle with refractive index near 1 and present a criterion that can be used to replace Mie scattering theory.
A new physical model of forward scattering of transmission of a polarized light beam in the atmosphere is established. Based on the incoherent light assumption, the double and multiple forward scattering theories are derived. To the symmetrical system, the effective Mueller matrix of the forward scattering of polarized light is obtained,.It is shown that only seven matrix elements are independent, the nine matrix elements are obtained by rotating independent elements. To validate the scattering model, the effective Mueller matrix of the forward scattering of polarized light of the transmission 10km in the atmosphere are simulated with Monte Carlo method, it is showed theatrical and numerical results are in good agreement.
On this basis the scattering model of polarized photons in the multilayered atmosphere is established. The Monte Carlo simulation of the propagation of polarized photons in the multilayered atmosphere is made based on the model.
We propose a scheme for optical realization of deterministic entanglement concentration of polarized photons. To overcome the difficulty due to the lack of sufficiently strong interactions between photons, teleportation is employed to transfer the polarization states of two photons onto the path and polarization states of a third photon, which is made possible by the recent experimental realization of the deterministic and complete Bell state measurement. Then the required positive operator-valued measurement and further operations can be implemented deterministically by using a linear optical setup.
由于自由空间量子密钥传输对将来利用卫星进行量子密钥分配并进而建立全球量子保密通信网具有重大意义,所以在自由空间进行量子密钥分配引起了人们的广泛关注和深入研究。本论文研究自由空间量子通信的相关理论问题,建立光子大气传输的适当的理论模型,分析光子偏振态如何受大气散射的影响,提出偏振光子纠缠浓缩的实现方案。本论文的完成将为自由空间量子通信的实施提供必要的理论支持和有价值的技术方案,这对于最终实现基于卫星的全球量子通信具有一定的理论意义和实用价值。论文主要研究成果有：
从Maxwell方程出发比较分析了Rayleigh近似与Mie散射的散射振幅与散射截面,得到当散射粒子的尺度参数较小时,Rayleigh散射与Mie散射符合的很好,可用Rayleigh散射代替Mie散射。同时比较分析了Born近似和Mie散射的散射振幅与散射截面,计算表明相对折射率在[1.01,1.09]之间的散射粒子,其尺度参数满足特定条件时可用Born散射代替Mie散射。这样,在满足条件的散射理论计算中,可避免繁琐的无穷级数计算。
针对自由空间量子通信,给出了前向直向散射的简化处理方案,推导了偏振光子Mie散射前向有效Mueller矩阵及各矩阵元之间的关系。
用矢量Monte Carlo方法模拟均匀大气中偏振光子的多次散射过程,得到表征大气信道特征的Mueller矩阵模拟图,并以此分析讨论了气溶胶粒子尺度对光子偏振态的影响。当粒子尺度较小时,光子的退偏效应很明显,光子偏振度对粒子尺度的变化非常敏感；当粒子尺度较大时,光子的偏振度较大,退偏效应弱,偏振度对粒子尺度的变化不敏感。
利用偏振光子的多次散射模型和经过改进的多层大气散射模型,研究了量子通信中光子与大气的相互作用过程,分析了单光子密钥分配过程中大气散射对偏振态的影响。结果表明,光子上行时偏振态保持的效果明显比下行时要好；光子在传输相同距离的情况下,高海拔位置比低海拔位置偏振态的变化幅度要小。
针对偏振纠缠光子在量子通信中由于偏振态变化而引起的纠缠度下降问题,提出了一种线性光学系统的理论方案,通信双方利用该系统可以确定性地从两对部分纠缠光子中提取出一对最大纠缠光子。这套装置借助于将两光子偏振态分别隐形传送到第三个光子的路径和偏振态上,通过实现单光子偏振态和路径态的操作,来完成两光子偏振态的操控,进而克服了光子间弱耦合带来的困难。
Traditional cryptography is based on complicated mathematical algorithms. However, with the development of quantum computers, the traditional cryptography could be deciphered, so communications security constitutes a conspicuous problem. Based on basic principles of quantum mechanics, quantum cryptography is "can not decipher" and "absolute security", therefore quantum cryptography can achieve a real sense of secure communications and an important research field of national security as well as the bright future for the development of information technology.
Because free-space quantum key transmission is of great significance to future quantum key distribution using satellites as well as to establishing a global network of quantum secure communication, free-space quantum key distribution has aroused widespread concern. This thesis studies the theory of free-space quantum communication and establishes the appropriate theoretical model of photon propagation in the atmosphere, analyzes the photon polarization vector by the atmospheric scattering effects. The completion of this thesis will provide necessary theoretical support and valuable technical program for free-space quantum communication, which will be of great importance for the eventual realization of satellite-based global quantum communication. Main conclusions of this thesis include:
We have analyzed and compared Rayleigh scattering and Mie scattering. It is shown that Rayleigh scattering and Mie scattering are in good agreement when the scale parameter is small. But when the scale parameter is large, dependence of Mie scattering intensity on wavelength is not obvious. We have analyzed and compared of Born approximation and Mie scattering of spherical particle with refractive index near 1 and present a criterion that can be used to replace Mie scattering theory.
A new physical model of forward scattering of transmission of a polarized light beam in the atmosphere is established. Based on the incoherent light assumption, the double and multiple forward scattering theories are derived. To the symmetrical system, the effective Mueller matrix of the forward scattering of polarized light is obtained,.It is shown that only seven matrix elements are independent, the nine matrix elements are obtained by rotating independent elements. To validate the scattering model, the effective Mueller matrix of the forward scattering of polarized light of the transmission 10km in the atmosphere are simulated with Monte Carlo method, it is showed theatrical and numerical results are in good agreement.
On this basis the scattering model of polarized photons in the multilayered atmosphere is established. The Monte Carlo simulation of the propagation of polarized photons in the multilayered atmosphere is made based on the model.
We propose a scheme for optical realization of deterministic entanglement concentration of polarized photons. To overcome the difficulty due to the lack of sufficiently strong interactions between photons, teleportation is employed to transfer the polarization states of two photons onto the path and polarization states of a third photon, which is made possible by the recent experimental realization of the deterministic and complete Bell state measurement. Then the required positive operator-valued measurement and further operations can be implemented deterministically by using a linear optical setup.
引文
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