连续变量四组份纠缠光场产生和量子保密通信研究
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摘要
量子信息是当今国际科学技术界的前沿研究课题，主要研究如何利用量子力学基本原理及量子态的特性，如量子纠缠和态叠加等，完成信息处理、计算与传送。量子纠缠是量子力学最重要的精华内容之一，它被认为是量子信息和量子计算的重要资源。利用量子纠缠，人们可以在信息与计算领域完成经典物理不可能完成的工作。利用量子纠缠，通讯双方可以实现对一个量子态的高保真度远程传输，即量子离物传态；利用量子纠缠，通信双方可以实现经典信息的高信道容量传输，即量子密集编码；甚至可以使原本不纠缠的量子系统在不直接相互作用的情况下产生纠缠，即量子纠缠交换。量子力学的诸多特性也应用到保密通信当中，可以从物理层面上达到真正意义的保密，实现绝对安全的量子密钥分发(Quantum key distribution，QKD)。各种利用量子纠缠的量子密钥分发方案，显示出独特的优越性。设计和实验实现有实际应用潜力的量子密钥分发方案，不仅有基础研究意义，而且有很强的应用需求。
量子信息科学根据所利用的量子变量的本征态具有分离谱或是连续谱结构区分为分离变量与连续变量两大类，连续变量和分离变量量子信息有着不同的特点与应用前景，各具特色，目前正在平行发展。量子信息研究先从分离变量开始，随后被扩展到连续变量领域。连续变量量子通信具有比特速率高等潜在优越性，近十年引起广泛的研究兴趣。但与分离变量相比，连续变量量子通信的实验研究仍相对滞后。虽然已利用连续变量两组份Einstein-Podolsky-Rosen(EPR)纠缠实现了无条件量子态离物传送、量子密集编码及量子纠缠交换等量子通信的重要基础实验，然而发展量子信息的关键是实现量子信息网络。获得多组份纠缠态是下一步发展量子信息网络的基本工作之一。
本论文的主要研究内容如下：
1．设计了连续变量四组份类Greenberger-Horne-Zeilinger(GHZ)纠缠态和类Cluster纠缠态产生系统，并完成了产生四组份类GHZ纠缠态和类Cluster纠缠态的实验研究。利用一对运转于参量反放大状态的非简并光学参量放大器，产生的四个正交分量压缩态光场(两束正交振幅压缩光，两束正交位相压缩光)，经适当的线性光学变换与量子非破坏(Quantum nondemolition，QND)耦合，通过对耦合光相对位相的控制，既产生了四组份类GHZ纠缠态，也产生了四组份类Cluster纠缠态。(Phys．Rev．Lett．98，070502(2007)；“中国科学”已接受)
2．提出一种利用明亮的EPR纠缠光束完成连续变量密集编码量子保密通信的方案。纠缠源被放置在接收者处，仅利用纠缠光束的一束(信号光)往返传输信息，而另一束光场(闲置光)被接收者保留用于解调信息。信息发送者同时将振幅和位相信号调制到信号光场上，然后将其返回到接收者处，接收者利用连续变量量子密集编码关联测量解调信号，因此信道容量被大大的提高。该方案可以直接利用量子纠缠突破连续变量量子保密通信的3 dB损耗极限(Phys．Rev．A 74，062305(2006))
3．直接利用光场的EPR关联实现了连续变量量子保密通信。通信双方共享一对明亮的EPR纠缠光束，随机选择测量各自所拥有的光场的正交振幅或正交位相分量，并利用各分量间的量子关联建立密钥。此方案无需信号调制，通过量子起伏的局域测量和公开比对建立密钥和发现窃听者。从信息理论证明了方案的安全性。实验结果显示，我们的裸码速率可达1×10~7bit／s。(Paper in preparing)
4．利用运转于阈值以上的非简并光学参量振荡器，制备了强度高达22row的频率非简并纠缠态光场。用非平衡Mach-Zehnder干涉仪所测得的正交振幅与正交位相的量子关联度分别为1.25dB和0.60dB。该方法提供了制备和检测频率可调谐高亮度纠缠态光场的有效途径。(Opt．Lett．31，1133(2006))
所完成的有所创新的研究工作如下：
1．设计了连续变量四组份类GHZ纠缠态和类Cluster纠缠态的实验产生系统，从理论上推导出四组份类Cluster纠缠态的完全不可分判据，计算了四组份纠缠对实验参量的依赖关系。首次从实验上获得了上述两类四组份纠缠态光场。
2．提出利用明亮EPR纠缠光束，通过双向传输实现连续变量密集编码量子保密通信的方案，通过理论计算证明了在高纠缠度下直接突破3 dB损耗极限的可能性。
3．提出一种利用EPR关联，无需信号调制，实现连续变量量子保密通信的新方案，并通过实验证实了该方案的可行性。
4．利用运转于阈值以上的非简并光学参量振荡器，制备了强度高达22 mW的频率非简并纠缠态光场，并利用一对非平衡Mach-Zehnder干涉仪测定了光场的纠缠度。
Quantum information is an advanced research topic in modern science and technology. The fresh subject devotes to exploit the fundamental principle of quantum mechanics and the amazing characteristic of quantum states, such as quantum entanglement and superposition of state etc, to perform the processing, computation and transmission of information. As well known, the phenomenon of entanglement is one of the quintessential features in quantum mechanics. It has been recognized that quantum entanglement is an important resource in quantum information and computation. Utilizing quantum entanglement, we can accomplish the impossible tasks in the frame of classical information and computation. Utilizing quantum entanglement, we can implement the disembodied transport of an unknown quantum state from one place to another remote place with high fidelity, i.e. quantum teleportation. Utilizing quantum entanglement, we can also improve the channel capacity of classical signal transmission by means of quantum channel, i.e. quantum dense coding, even we can entangle two quantum systems that have never directly interacted with each other through entanglement swapping. The fundamental properties of quantum physics have been applied to cryptography. Quantum cryptography based on quantum mechanics can ensure genuine security of communication in principle and realize the absolutely secure quantum key distribution (QKD). A variety of quantum key distribution protocols depending on quantum entanglement exhibit especial advantages. Designing and experimentally realizing quantum key distribution have not only the significance for the fundamental research but also the potential application requirement.
According to that the eigenstates of applied quantum systems are with discrete or continuous spectrum construction, quantum information is divided into two types of discrete variables (dv) and continuous variables (cv). They have different features and application potentials. Both of them are developing in parallel. Generally, quantum information starts from discrete variables originally, and then is extended into the field of continuous variables. The cv quantum communication has attracted wide interests due to its potential advantages such as high bit transmission rates. However, with the comparison to the dv system, the experimental investigation of cv quantum communication is relatively lagging. So far, the fundamental experiments, such as unconditional quantum teleportation, quantum dense coding and quantum entanglement swapping, have been realized with cv Einstein-Podolsky-Rosen (EPR) entanglement. However, the key for developing quantum information is to realize quantum information network. For developing quantum information network a most important step is to generate multipartite entangled states experimentally.
The main research contents of the thesis are as followings:
1. We designed the generation system of cv quadripartite GHZ-like and Cluster-like entangled states and accomplished the experiment generating quadripartite GHZ-like and Cluster-like entangled states. We theoretically and experimentally demonstrated that the two different types of quadripartite entangled states can be obtained by the linearly optical transformation of four squeezed states (two amplitude-quadrature squeezed states and two phase-quadrature squeezed states) produced from a pair of nondegenerate optical parametric amplifiers operating at deamplification under appropriate phase relations. (Phys. Rev. Lett. 98, 070502 (2007); Science in China, accepted)
2. We proposed a scheme of continuous-variable quantum key distribution, in which the bright EPR entangled optical beams are utilized. The source of the entangled beams is placed inside the receiving station, then a half of the entangled beams is transmitted with round trip between the receiver and the sender and the other half are retained by the receiver which is never opened. Two sets of signals respectively modulated on the amplitude and phase quadratures of the signal beam by the sender are simultaneously extracted by the authorized receiver with the scheme of the dense-coding correlation measurement for continuous quantum variables, thus the channel capacity is significantly improved. The proposed scheme can beat the 3 dB loss limit of the cv quantum key distribution when the high quantum entanglement is utilized. (Phys. Rev. A 74, 062305 (2006))
3. We implemented the cv quantum key distribution using the EPR correlation of the optical field directly. Two communication parties share a pair of bright EPR entangled beam and measure the amplitude or phase quadratures of their own optical fields randomly. Then, the secret key is established by means of quantum correlation between their amplitude and phase quadratures. In the proposed QKD scheme without the signal modulation the secret key is established and the eavesdropper is discovered through the local measurement of quantum fluctuations and the public comparing of the measured data. The security of the scheme was proved with information theory. (Paper in preparing)
4. The frequency-nondegenerate entangled beams with total intensity of 22 mW were produced from a nondegenerate optical parametric oscillator operating above threshold. The correlation degree of amplitude-quadrature and phase-quadrature measured by unbalance Mach-Zehnder interferometer are 1.25 dB and 0.60 dB, respectively. The experimental design provides an effective approach to prepare and detect the frequency tunable entangled optical field high intensity.
The completed creative works are as follows:
1. We designed the experimental generation system of cv quadripartite GHZ-like and Cluster-like entangled states, deduced the fully inseparability criteria of quadripartite Cluster-like entangled states theoretically and calculated the dependences of quadripartite entanglement on experimental parameters numerically. We experimentally obtained the two kinds of cv quadripartite entangled optical fields for the first time.
2. We proposed a scheme of continuous-variable quantum key distribution utilizing the bright Einstein-Podolsky-Rosen entangled optical beams and roundtrip transmission. The possibility of beating 3 dB loss limit with higher entanglement was theoretically proved.
3. We proposed a scheme of continuous variable quantum key distribution without signal modulation using EPR correlation directly and experimentally proved the feasibility of the scheme.
4. We prepared the frequency-nondegenerate entangled optical field with the total intensity of 22 mW by means of nondegenerate optical parametric oscillator operating above threshold and measured the entanglement degree with a pair of unbalanced Mach-Zehnder interferometers.
量子信息科学根据所利用的量子变量的本征态具有分离谱或是连续谱结构区分为分离变量与连续变量两大类，连续变量和分离变量量子信息有着不同的特点与应用前景，各具特色，目前正在平行发展。量子信息研究先从分离变量开始，随后被扩展到连续变量领域。连续变量量子通信具有比特速率高等潜在优越性，近十年引起广泛的研究兴趣。但与分离变量相比，连续变量量子通信的实验研究仍相对滞后。虽然已利用连续变量两组份Einstein-Podolsky-Rosen(EPR)纠缠实现了无条件量子态离物传送、量子密集编码及量子纠缠交换等量子通信的重要基础实验，然而发展量子信息的关键是实现量子信息网络。获得多组份纠缠态是下一步发展量子信息网络的基本工作之一。
本论文的主要研究内容如下：
1．设计了连续变量四组份类Greenberger-Horne-Zeilinger(GHZ)纠缠态和类Cluster纠缠态产生系统，并完成了产生四组份类GHZ纠缠态和类Cluster纠缠态的实验研究。利用一对运转于参量反放大状态的非简并光学参量放大器，产生的四个正交分量压缩态光场(两束正交振幅压缩光，两束正交位相压缩光)，经适当的线性光学变换与量子非破坏(Quantum nondemolition，QND)耦合，通过对耦合光相对位相的控制，既产生了四组份类GHZ纠缠态，也产生了四组份类Cluster纠缠态。(Phys．Rev．Lett．98，070502(2007)；“中国科学”已接受)
2．提出一种利用明亮的EPR纠缠光束完成连续变量密集编码量子保密通信的方案。纠缠源被放置在接收者处，仅利用纠缠光束的一束(信号光)往返传输信息，而另一束光场(闲置光)被接收者保留用于解调信息。信息发送者同时将振幅和位相信号调制到信号光场上，然后将其返回到接收者处，接收者利用连续变量量子密集编码关联测量解调信号，因此信道容量被大大的提高。该方案可以直接利用量子纠缠突破连续变量量子保密通信的3 dB损耗极限(Phys．Rev．A 74，062305(2006))
3．直接利用光场的EPR关联实现了连续变量量子保密通信。通信双方共享一对明亮的EPR纠缠光束，随机选择测量各自所拥有的光场的正交振幅或正交位相分量，并利用各分量间的量子关联建立密钥。此方案无需信号调制，通过量子起伏的局域测量和公开比对建立密钥和发现窃听者。从信息理论证明了方案的安全性。实验结果显示，我们的裸码速率可达1×10~7bit／s。(Paper in preparing)
4．利用运转于阈值以上的非简并光学参量振荡器，制备了强度高达22row的频率非简并纠缠态光场。用非平衡Mach-Zehnder干涉仪所测得的正交振幅与正交位相的量子关联度分别为1.25dB和0.60dB。该方法提供了制备和检测频率可调谐高亮度纠缠态光场的有效途径。(Opt．Lett．31，1133(2006))
所完成的有所创新的研究工作如下：
1．设计了连续变量四组份类GHZ纠缠态和类Cluster纠缠态的实验产生系统，从理论上推导出四组份类Cluster纠缠态的完全不可分判据，计算了四组份纠缠对实验参量的依赖关系。首次从实验上获得了上述两类四组份纠缠态光场。
2．提出利用明亮EPR纠缠光束，通过双向传输实现连续变量密集编码量子保密通信的方案，通过理论计算证明了在高纠缠度下直接突破3 dB损耗极限的可能性。
3．提出一种利用EPR关联，无需信号调制，实现连续变量量子保密通信的新方案，并通过实验证实了该方案的可行性。
4．利用运转于阈值以上的非简并光学参量振荡器，制备了强度高达22 mW的频率非简并纠缠态光场，并利用一对非平衡Mach-Zehnder干涉仪测定了光场的纠缠度。
Quantum information is an advanced research topic in modern science and technology. The fresh subject devotes to exploit the fundamental principle of quantum mechanics and the amazing characteristic of quantum states, such as quantum entanglement and superposition of state etc, to perform the processing, computation and transmission of information. As well known, the phenomenon of entanglement is one of the quintessential features in quantum mechanics. It has been recognized that quantum entanglement is an important resource in quantum information and computation. Utilizing quantum entanglement, we can accomplish the impossible tasks in the frame of classical information and computation. Utilizing quantum entanglement, we can implement the disembodied transport of an unknown quantum state from one place to another remote place with high fidelity, i.e. quantum teleportation. Utilizing quantum entanglement, we can also improve the channel capacity of classical signal transmission by means of quantum channel, i.e. quantum dense coding, even we can entangle two quantum systems that have never directly interacted with each other through entanglement swapping. The fundamental properties of quantum physics have been applied to cryptography. Quantum cryptography based on quantum mechanics can ensure genuine security of communication in principle and realize the absolutely secure quantum key distribution (QKD). A variety of quantum key distribution protocols depending on quantum entanglement exhibit especial advantages. Designing and experimentally realizing quantum key distribution have not only the significance for the fundamental research but also the potential application requirement.
According to that the eigenstates of applied quantum systems are with discrete or continuous spectrum construction, quantum information is divided into two types of discrete variables (dv) and continuous variables (cv). They have different features and application potentials. Both of them are developing in parallel. Generally, quantum information starts from discrete variables originally, and then is extended into the field of continuous variables. The cv quantum communication has attracted wide interests due to its potential advantages such as high bit transmission rates. However, with the comparison to the dv system, the experimental investigation of cv quantum communication is relatively lagging. So far, the fundamental experiments, such as unconditional quantum teleportation, quantum dense coding and quantum entanglement swapping, have been realized with cv Einstein-Podolsky-Rosen (EPR) entanglement. However, the key for developing quantum information is to realize quantum information network. For developing quantum information network a most important step is to generate multipartite entangled states experimentally.
The main research contents of the thesis are as followings:
1. We designed the generation system of cv quadripartite GHZ-like and Cluster-like entangled states and accomplished the experiment generating quadripartite GHZ-like and Cluster-like entangled states. We theoretically and experimentally demonstrated that the two different types of quadripartite entangled states can be obtained by the linearly optical transformation of four squeezed states (two amplitude-quadrature squeezed states and two phase-quadrature squeezed states) produced from a pair of nondegenerate optical parametric amplifiers operating at deamplification under appropriate phase relations. (Phys. Rev. Lett. 98, 070502 (2007); Science in China, accepted)
2. We proposed a scheme of continuous-variable quantum key distribution, in which the bright EPR entangled optical beams are utilized. The source of the entangled beams is placed inside the receiving station, then a half of the entangled beams is transmitted with round trip between the receiver and the sender and the other half are retained by the receiver which is never opened. Two sets of signals respectively modulated on the amplitude and phase quadratures of the signal beam by the sender are simultaneously extracted by the authorized receiver with the scheme of the dense-coding correlation measurement for continuous quantum variables, thus the channel capacity is significantly improved. The proposed scheme can beat the 3 dB loss limit of the cv quantum key distribution when the high quantum entanglement is utilized. (Phys. Rev. A 74, 062305 (2006))
3. We implemented the cv quantum key distribution using the EPR correlation of the optical field directly. Two communication parties share a pair of bright EPR entangled beam and measure the amplitude or phase quadratures of their own optical fields randomly. Then, the secret key is established by means of quantum correlation between their amplitude and phase quadratures. In the proposed QKD scheme without the signal modulation the secret key is established and the eavesdropper is discovered through the local measurement of quantum fluctuations and the public comparing of the measured data. The security of the scheme was proved with information theory. (Paper in preparing)
4. The frequency-nondegenerate entangled beams with total intensity of 22 mW were produced from a nondegenerate optical parametric oscillator operating above threshold. The correlation degree of amplitude-quadrature and phase-quadrature measured by unbalance Mach-Zehnder interferometer are 1.25 dB and 0.60 dB, respectively. The experimental design provides an effective approach to prepare and detect the frequency tunable entangled optical field high intensity.
The completed creative works are as follows:
1. We designed the experimental generation system of cv quadripartite GHZ-like and Cluster-like entangled states, deduced the fully inseparability criteria of quadripartite Cluster-like entangled states theoretically and calculated the dependences of quadripartite entanglement on experimental parameters numerically. We experimentally obtained the two kinds of cv quadripartite entangled optical fields for the first time.
2. We proposed a scheme of continuous-variable quantum key distribution utilizing the bright Einstein-Podolsky-Rosen entangled optical beams and roundtrip transmission. The possibility of beating 3 dB loss limit with higher entanglement was theoretically proved.
3. We proposed a scheme of continuous variable quantum key distribution without signal modulation using EPR correlation directly and experimentally proved the feasibility of the scheme.
4. We prepared the frequency-nondegenerate entangled optical field with the total intensity of 22 mW by means of nondegenerate optical parametric oscillator operating above threshold and measured the entanglement degree with a pair of unbalanced Mach-Zehnder interferometers.
引文
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