基于斐波那契螺线的轨道角动量纠缠态的量子保密通信研究

For the difficulty in finding the helical structure corresponding to orbital angular momentum (OAM) entangled states in nature, in this projection, we study the theory of quantum private communication based on Fibonacci-valued OAM entangled states using the arrangements of the sunflower’s seeds. To break through the constraints and limitations of information encoding and decoding using orbital angular momentum, we explore the high-order and sparse Fibonacci and Lucas matrix coding, and achieve high-capacity, decoy-state, and measurement-device-independent quantum communication, by revealing the Fibonacci helicity of the arrangement of the sunflower’ s seeds step by step. The main contents are as follows: 1) the theoretical study of the preparation of high-quality quantum entanglement states based on Fibonacci helicity, the simplification of the high-order Fibonacci and Lucas matrices and quantum storage of OAM entanglement, 2) to find the ways to reduce the influence of dark counts in quantum private communication and to extend the range of applications of high-order Fibonacci and Lucas matrices, 3) to study the application of OAM in high-capacity, decoy-state, and measurement-device-independent quantum private communication. Through the study of this project, a series of original research results can be formed, which provide important theoretical basis and technical support for the application of large-scale quantum private communication of orbital angular momentum to free space.

针对在自然界中很难找到相关的螺旋性结构对光子轨道角动量响应的量子保密通信的难题，本项目围绕研究“基于向日葵种子排列的斐波那契螺旋性的轨道角动量纠缠态的量子保密通信理论研究”为核心，突破以往在对轨道角动量进行信息编码及解码的束缚和局限，探索高阶稀疏斐波那契和卢卡斯矩阵编码，分阶段、有步骤地揭示向日葵种子排列的斐波那契螺旋性来实现高容量的、诱骗态的、与测量设备无关的量子保密通信。主要内容包括：1）开展基于斐波那契螺旋性的高品质的量子纠缠态制备的理论研究和高阶斐波那契和卢卡斯矩阵的简化及其用于量子存储的理论研究，2）寻找减少量子通信过程中暗计数的影响和扩展高阶斐波那契和卢卡斯矩阵计算应用范围的途径，3）研究基于光子轨道角动量的应用诱骗态的、测量设备无关的、高容量的量子保密通信。通过本项目的研究，形成一系列原创性研究成果，为轨道角动量的大规模的量子保密通信应用到自由空间提供重要理论依据和技术支撑。

本项目将光子轨道角动量（OAM）的特殊结构和二维非线性晶体的和频出发，引入自然界中的向日葵种子的排列方式的数模—大自然中的Fibonacci数列，探索出了实用于自由空间量子通信的高品质OAM纠缠态，还可用于修复轨道角动量态。基于Fibonacci和Lucas矩阵编码及其表示，结合研究低阶Fibonacci和Lucas矩阵的结构与行列式值，构造了可逆的高阶Fibonacci和Lucas矩阵，数量级地提高OAM纠缠态编码容量。同时，选择合适的Fibonacci和Lucas数来实现自由空间的更远距离和更低错率的纠缠态光子传输，并从根本上降低生成密钥存储的费用。最后，应用在诱骗态、与测量设备无关量子密钥分发协议中，解决理想单光子源的问题和消除发送端和接收端间的基校准；并进一步提升系统容量以及频谱效率，满足未来量子通信需求需要探索新技术。