基于交叉克尔非线性的量子信息处理

Based on cross-Kerr nonlinearities, the project intends to study the construction of the photonic quantum logical gates and its applications for quantum information processing. Exploiting effective cross-Kerr nonlinear interaction between signal photons and the probe coherent state, which is established in Kerr media, and the appropriate photonic circuits and measurement methods, the entanglement of the paths, polarization or other degrees of freedom between the signal photons can be generated and converted to each other, and thus the quantum logical gates and quantum information processing tasks with high efficiency and low cost to run even in a real environment can be realized. The project will study time evolution of the real physical system of photons, coherent states and other optical elements such as photon detectors, and exploit homodyne measurement or photon quantum nondemolition measurement and feed forward techniques to overcome the disadvantageous influence resulted from environment noise and imperfect elements in the construction of the quantum logical gates and the tasks of quantum information processing, and then increase the correct probabilities and the efficiencies of the presented schemes. Depending on the entanglement between these degrees of freedom achieved by cross-phase modulation in Kerr media, some schemes of quantum information processing will be designed, for instance, quantum logical gates, quantum state preparation and analysis, and quantum key distribution. Furthermore, we will also think about the quantum measurement, which is a fundamental problem of quantum mechanics, and consider to study and design the photon-number nondemolition measurement method for the systems involved in this project, and apply it to construct quantum logical gates and the schemes of quantum information processing mentioned above. This project will play an important role on the developments of theoretical research on the field of quantum information and accelerate the pace of the practical applications of quantum information processing, and cultivate a high-level research team with rational construction.

基于强、弱交叉克尔非线性（辅以探测相干态），拟研究光子之间的可规模化的概率的或确定的量子逻辑门以及相关的量子信息处理应用。借助有效的交叉克尔非线性效应以及适宜的光子线路和测量方法，实现光子之间的路径、偏振等自由度的纠缠及之间的转换，构造能在理想条件下和实际环境中高效率低成本地运行的量子信息处理方案。对信号光子、探测相干态、光子探测器等光学元件以及环境的开放系统进行研究，应用非平衡零拍差测量以及前馈技术等克服环境噪声和不完美元件的影响，提高实现的成功率与效率。依赖交叉克尔效应的相位调制所实现的光子纠缠，设计量子逻辑门、量子态制备分析以及量子密钥分配等量子信息处理方案。采用主动稳定干涉仪方法实时监测反馈，进而保证干涉的稳定性。研究适宜的光子数探测方案，应用于量子信息处理方案中。本项目将推动量子信息理论的发展和加快量子信息处理实际应用的步伐，同时造就出一支高水平的、结构合理的研究队伍。

本项目以极化比特控制相位门、宇称分析门、分布纠缠门、局域纠缠门等量子逻辑门为基础，提出了基于弱交叉克尔非线性的多光子极化比特量子傅里叶变换、三光子极化比特Fredkin门、多光子极化簇态的制备、四光子极化退相干自由态的制备、多光子极化态的容错传输以及量子安全直接通信等量子信息处理方案。借助有效的交叉克尔非线性效应以及适宜的光子线路，实现光子之间的路径、极化等自由度的纠缠及之间的转换。应用适宜的测量方案以及前馈操作等克服环境噪声和不完美元件的影响，提高实现的成功概率与效率。这些方案具有效率高、线路简单、成功率高、抵抗退相干等优点。.应用极化比特 CP π/2 门和阿达马门，我们提出了一个两光子极化比特量子傅里叶变换方案。以此为基础进行了推广，应用级联极化比特 CP π/2^i (i = 1, 2, … , n-1) 门和阿达马门的组合，我们提出了多光子极化比特量子傅里叶变换方案。应用基于交叉克尔非线性构造的路径纠缠门、交换门、合并门，我们提出了一个三光子极化比特Fredkin门方案。.基于极化比特控制相位反转门、分布纠缠门以及简化纠缠门等基本逻辑门，我们提出了多光子极化簇态的制备、链接、解链等方案。应用一个空间纠缠进程、两个极化纠缠进程、一个检测进程，我们提出了四光子极化退相干自由态的构造方案，它可以用来构造最小的光学退相干自由子空间。.基于极化纠缠模式和空间纠缠模式之间的转换，我们提出了一个多光子极化态的传送方案，容错线路的应用使得多光子态可从某一地方无损地传送到另一个地方。应用光子极化贝尔态作为量子信息载体，容错分发贝尔光子对，两方共享贝尔光子对，我们提出了量子直接安全通信方案；应用无损测量检测光子，节省物理资源，方案效率得到大幅提升。.上述研究证明了基于交叉克尔非线性构造通用量子逻辑门、制备光子纠缠态、实现量子安全通信等量子信息处理方案的可行性。

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