本项目主要研究与量子纠缠和非局域性相关的一些重要理论及应用问题，包括利用特殊酉群的生成元和海森堡-威尔算子的均值分析表示量子态的Bloch向量，结合测量与量子态系综的对应关系，构造基于可观测量的任意量子系统的纠缠检测方案、Bell不等式以及基于测量的纠缠和非局域性度量的统一表达式，从而研究量子纠缠和非局域性（包括束缚纠缠、多体真正纠缠和多体真正非局域性）的检测、度量的计算和估计；计算Bell不等式的最大违背值及其在局域过滤操作下的衍化，进而定量地讨论量子非局域性与量子保密通信安全性和通信复杂性的关系等。本项目的相关理论成果不仅有利于分析量子纠缠和非局域性与经典关联的本质差别，还有益于定量讨论量子通信的可行性及有效性。

This program mainly study some important theoretical problems and applications about quantum entanglement and quantum nonlocality. By representing quantum density operators in terms of the generators of the special unitary group and the Heisenberg-Wely operators we define Bloch vectors. Then using the relationship between measurement and quantum ensemble representations, together with the Bloch representations we construct entanglement detection protocols, Bell inequalities, and unified entanglement and quantum nonlocality measures based on observables. The detection of (multipartite genuine) quantum entanglement and quantum nonlocality and the computation of corresponding measures will be investigated. The maximal violations of Bell inequalities and its behavior under the local filtering operations will be also studied, by which we discuss the relationship between quantum nonlocality and quantum secret communication and quantum complexity quantitatively. The results of this program will not only be beneficial for understanding the nature and the differences between quantum entanglement, quantum nonlocality and classical correlations, but also help discuss the feasibility and the effectiveness of quantum communications.