多光子纠缠态的制备和多量子比特系统的Bell型不等式

发布时间：2018-06-14 20:44

本文选题：量子纠缠 + 多光子纠缠态　；参考：《河北师范大学》2016年博士论文

【摘要】：量子纠缠是一种切实的物理资源,量子态的纠缠特性是量子力学区别于经典力学的最基本特征,对量子纠缠的研究具有重大的科学意义.本文主要研究多光子纠缠态的制备和多量子比特系统的Bell型不等式,具体研究成果为:1.基于参量下转换源、克尔非线性介质和线性光学器件,我们提出一个高效的四光子Greenberger-Horne-Zeilinger(GHZ)态的制备与纯化方案.首先,我们研究如何从参量下转换源产生的两对纠缠光子制备出一个包含偏振纠缠和空间纠缠的四光子超纠缠GHZ态.接着,在考虑存在退极化噪声的情况下进一步给出用空间纠缠纯化偏振纠缠方案.2.我们提出一个高效制备六光子超纠缠态方案,制备的超纠缠态包含偏振纠缠和空间纠缠.考虑参量下转换源产生三对纠缠光子情况,我们设计量子线路演化光子态.因为方案中考虑了光子的全部可能状态,所以方案有很高的效率.3.基于线性光学和弱非线性介质,我们提出了一类多光子纠缠态的制备方案.方案中,我们在非线性相互作用过程中仅引入了两个很小的相位角.在不考虑消相干的情况下,我们计算测量过程中的出错概率,结果表明即使光子数很大时其最大出错概率也可以任意小.4.我们提出一个弱非线性机制下制备多光子数态纠缠方案.在非线性相互作用过程中引入的相位角的最大值与光子数成正比,同时通过约束相位角的大小以保障方案满足弱非线性机制.同样,在不考虑消相干的情况下我们计算测量过程中的出错概率,结果表明当前方案是可行的.5.我们研究一类重要的四量子比特纠缠态的纠缠度量及其对一种指定的Bell型不等式的量子违背.结果表明存在一类四量子比特纠缠态全部违背指定的不等式,其纠缠度量随着Bell算子期望值的增加先减小而后增加,两者的关系曲线是一条平滑曲线.6.基于Clauser-Horne-Shimony-Holt不等式,我们提出一种构建多量子比特系统Bell型不等式的方法.不等式结构简单便于实验,尤其是选择一组给定的测量环境可以得到一组紧凑的Mermin型不等式.以这组Mermin型不等式为例,我们讨论了广义GHZ(GGHZ)态和两类常见的混合纠缠态对不等式的违背.同时,我们还研究了四量子比特GGHZ态的纠缠度量与其量子违背值间的关系.
[Abstract]:Quantum entanglement is a practical physical resource. The entanglement characteristic of quantum state is the most basic characteristic of quantum mechanics which is different from classical mechanics. It is of great scientific significance to the study of quantum entanglement. In this paper, we mainly study the preparation of multiphoton entangled states and Bell type inequalities for multiquantum bit systems. The specific research results are: 1: 1. Based on parametric downconversion sources, Kerr nonlinear media and linear optical devices, we propose an efficient scheme for the preparation and purification of four-photon Greenberger-Horne-ZeilingerGHZ states. First, we study how to produce a four-photon hyperentangled GHz state with polarization entanglement and spatial entanglement from two pairs of entangled photons generated from the parametric down-conversion source. Then, considering the presence of depolarization noise, the scheme of polarization entanglement purification by space entanglement. 2. We propose an efficient scheme for the preparation of six-photon hyperentangled states, which include polarized entanglement and spatial entanglement. Considering the generation of three pairs of entangled photons from the parametric down-conversion source, we design a quantum circuit evolving photon state. Because all possible states of photons are considered in the scheme, the scheme is highly efficient. 3. Based on linear optics and weakly nonlinear media, we propose a scheme for the preparation of a class of multiphoton entangled states. In the scheme, only two small phase angles are introduced in the nonlinear interaction process. Without considering decoherence, we calculate the error probability in the measurement process. The results show that the maximum error probability can be as small as. 4 even if the photon number is large. We propose a weak nonlinear scheme for the preparation of multiphoton number state entanglement. The maximum value of the phase angle introduced in the nonlinear interaction process is proportional to the number of photons, and the scheme satisfies the weak nonlinear mechanism by constraining the magnitude of the phase angle. Similarly, we calculate the error probability in the measurement process without considering the decoherence. The results show that the current scheme is feasible. We study the entanglement metric of an important four-bit entangled state and its quantum violation of a specified Bell type inequality. The results show that a class of quaternion entangled states all violate the specified inequality, and the entanglement metric decreases first and then increases with the increase of the expected value of Bell operators. The relation curve between the two is a smooth curve .6. Based on Clauser-Horne-Shimony-Holt inequality, we propose a method to construct Bell type inequalities for multi-quantum bit systems. The structure of the inequality is simple and convenient for experiment, especially, a set of compact Mermin type inequalities can be obtained by selecting a set of given measuring environments. Taking this set of Mermin type inequalities as an example, we discuss the violation of inequalities by generalized GHZ GGHZ) states and two common mixed entangled states. At the same time, we also study the relationship between the entanglement metric of the four-bit GGHZ state and its quantum violation.
【学位授予单位】：河北师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413.1

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