非定域性，量子关联相关问题研究

With the progress of quantum information, nonlocality,quantum correlaiton have more and more applications. This project foucus on two subjects. One is characterizing nonlocality and linking nonlocality to random number generation in higher dimension system( more obervers, more local observables or more measurement outcomes). Based on the geometrical structure of correlation polytope, we propose the methods to extend Bell inequalities in lower dimension into ones in higher dimension and give the algebraic expressions of Bell inequalities. The maximal violation factors and the state with maximal violation factors will been computed and check whether the maximal violation factors are larger than the maximal violation factors of MARB inequalities and the state with maiximal violation factors are generalized GHZ states or not. Then we will propose the more efficient protocol of random number extension,and find the relation between nonlocality and randomness. .The other is determine the quantum correlation and try to answer what on earth is the reason of speedup of quantum information. Quantum correlation attraced more and more attenetion because it accomplishes some quantum information task in which entanglement is not been involved. We have suggested a norm-based measurement of quantum correlation which is easy to calculate and to generalize to higher dimension. In project, we will look for the more suitable norm of operators such that the norm-based measurement of quantum correlation has not only physical interest but also can be verify at labboratory. Furthermore, we will find the method to construct the witnesses for quantum correlation based on some experience of our work on consturctiong bell inequalities.

随着量子信息学科的发展，非定域性、量子关联有着越来越重要的作用。本课题包含两方面内容，其一是高维非定域性的刻画。利用关联多面体的几何性质来刻画高维情形下的非定域性。检验违反因子是否能突破MARB的违反因子；并且达到最大违反的量子态是否一定是广义GHZ态。并以此为基础上，研究高维情形下的非定域性与量子随机性之间的关系。拓展非定域性与随机性之间的联系，发掘非定域性的应用。其二是量子关联的刻画。量子信息处理能力指数增加的原因是什么？这个问题一直是人们追问的。在得知量子纠缠不是唯一因素后，人们发现量子关联的重要性。但是对量子关联的刻画并不令人满意。我们通过算子范数给出了一个较为普适，易于计算的量子关联度量。在此基础上，将研究基于范数的量子关联度量的物理含义；如何构造量子关联的目击算符来实验验证量子关联；并且在多粒子情形下，给出量子关联的分类。

非定域性是量子物理的核心研究内容之一。本课题着重于研究多粒子体系非定域性的判定及实验检验的相关课题。课题的主要结果是，给出了多粒子体系的紧的齐次贝尔不等式的结构特点，在此基础上给出了构造多粒子贝尔不等式的方法，并给出了一组只包含4项的多粒子不等式。在检验4粒子dick态的非定域性试验中，我们的不等式的简洁、方便的特性得到证实。每个贝尔不等式的算符模式，都对应于一个相容图。通过对相容图性质的研究，给出了多粒子体系中，各个子系之间非定域性的相互约束关系。另一方面，量子导引及其实验验证是这个课题的另一个主题。通过对导引椭球几何性质的研究，提出了导引半径用于量化量子导引。并在实验上证实了非对称的量子导引态。