局域高斯操作辅助下的连续变量量子纠缠蒸馏研究

Quantum entanglement is one of the most important resources in Quantum Information Processing, however, entanglement is quite a fragile resource and it may be easily disturbed by the environmental noises. To this point, entanglement distillation, a probabilistic process, is proposed to repair entanglement from noise, using physical feasible quantum resources. To distill Gaussian continuous variable entanglement, non-Gaussian resources must be introduced. Photon subtraction (PS) is just such a kind of non-Gaussian operation and has already been found in quantum teleportation, quantum state preparation and many other quantum information processing tasks. Recently, we find that local gaussian operations, though known to be useless on their own for distilling Gaussian entangled state, can be used to enhance state-of-art entanglement distillation, improving both the distillation probability and output entanglement. Such a result sheds more light on the usefulness of local Gaussian operations and opens new direction in distilling continuous variable entangled states. The aim of this proposal is to continue our research in distillation of continuous variable entanglement with photon subtraction and local Gaussian operations. To be specific:(1) we will derive the corresponding threshold condition for beamsplitter in local-Gaussian-operation-assisted distillation of exetremely strong two mode squeezed state. (2) we will specify the effect of phase-random noise on the PS technique and finally solve the problem of distillation of Gaussian entangled state which is disturbed by general noise channel. (3) we will study the optimized combination of entanglement swapping and entanglement distillation. These results will be benefical for further developing more-efficient entanglement based quantum communication process. Finally, as an example, we will apply our method to a specific quantum channel , 50 km optic fiber with the typical loss of 0.20dB/km , and propose the optimized scheme for entanglement distribution.

量子纠缠是量子信息中的重要资源，但是纠缠本身十分脆弱，它极易受到噪声的影响而坍缩。纠缠蒸馏是采用物理允许的手段对纠缠进行概率性修复的过程。连续变量高斯纠缠态的蒸馏需要用非高斯操作才能实现。在光学连续变量系统中，光子擦除技术是原理简单、实验相对容易的非高斯技术，也是在量子信息处理中有着广泛应用的重要技术。最近，我们发现局域高斯操作可以大大提高连续变量系统中光子擦除的概率和输出纠缠的质量。这给连续变量纠缠蒸馏增添了新的内容。本项目拟继续研究高斯操作辅助下纠缠蒸馏：(1)研究局域操作下基于光子擦除纠缠蒸馏的阈值条件，解决强纠缠态输入条件下蒸馏问题；(2)研究位相噪声对纠缠光子擦除的影响，解决广义信道条件下的纠缠蒸馏问题；(3)研究纠缠蒸馏与纠缠交换融合，解决纠缠蒸馏与量子通讯的优化组合问题。我们将纠缠蒸馏应用到50公里光纤信道中的纠缠分发过程，研究并提出高效的纠缠分发方案。

连续变量量子纠缠蒸馏是近年来兴起的一个重要的研究方向，其提出背景即是解决量子纠缠在有损信道中的传输时的纠缠态的损失和纠缠态质量下降问题。本项目主要针对连续变量两模量子纠缠态的蒸馏进行研究。连续变量量子纠缠以高斯型纠缠最为常见，对于高斯型连续变量量子纠缠态的蒸馏研究必须借助于非高斯操作才能实现。而最典型的非高斯操作即为光子的擦除操作。我们提出了局域压缩操作对于光子擦除操作的增强作用并以此为出发点，就强压缩纠缠输入时的纠缠蒸馏、位相随机涨落时的纠缠蒸馏以及纠缠蒸馏与纠缠交换的融合问题展开了研究，在新的条件下验证了局域高斯操作对于非高斯型纠缠蒸馏的改进作用。具体地：.（1）强压缩纠缠输入的蒸馏问题。我们提出了含一阶量的两模高斯纠缠态的密度矩阵元的并行计算算法，研制了基于MATLAB的并行计算程序，形成了对一阶量非零每模有效截断在14维和一阶量为零每模有效截断在24维的任意两模高斯纠缠态数值模拟能力。研究了强压缩纠缠(压缩度11.20dB)的两模压缩态的有效蒸馏方法，提出了基于双边光子逆擦除(光子增加)型纠缠蒸馏办法，在蒸馏成功概率和蒸馏产出质量两个方面都得到了大幅度的改进。.（2）位相随机涨落方面，利用主方程方法解出了两模连续变量量子纠缠态在位相随机涨落信道中的动力学演化情况，采用密度矩阵转置负定理论解析出位相随机噪声对于纠缠态的影响。设计了位相随机涨落信道条件下的连续变量量子纠缠蒸馏方案，并将位相随机涨落与振幅衰减噪声相结合，证明了光子擦除操作在广义信道条件下进行纠缠蒸馏的普适性。另外，就局域压缩操作对两份纠缠蒸馏过程中的改进作用也进行了定量刻画。.（3）纠缠蒸馏与纠缠交换融合方面。纠缠交换是一个高斯过程，我们从相空间角度推导出高斯型两模纠缠态在纠缠交换过程中的动力学演化。纠缠蒸馏是一个非高斯过程，我们利用高斯态线性组合的方式解析出纠缠蒸馏的相空间表示形式。我们以50公里为例，将50公里平均分成相等4段。利用Wigner函数的线性性质，我们对先纠缠蒸馏后纠缠交换和先纠缠交换后纠缠蒸馏两种情况进行定量刻画。通过对以上两种情况的产出纠缠进行比对，证明了先蒸馏后交换是最优的。这为实际条件下纠缠蒸馏与量子通讯的有效结合奠定了基础。