解说量子纠缠理论

量子纠缠态在量子信息处理，如量子隐形传态、量子密集码、量子纠错、量子保密通信、量子计算等过程中起了十分重要的作用.量子纠缠理论主要研究量子态的纠缠刻画、分类及其在量子信息处理中的应用.文章介绍了量子纠缠理论中的一些基本概念和结果，其中包括：量子力学的实在性、局域性的讨论与Bell不等式的联系，Bell不等式与量子态可分性间的关系；纯态和混合态可分性的定义及若干判别准则(包括矩阵正映照方法、部分转置判据、约化判据、重排判据、纠缠见证、协方差判据及局域测不准关系判据)；部分纠缠度量的介绍(包括纠缠形成、并发度、相对熵、负度、缠结和纠缠帮助，以及纠缠度量的计算和上下界的估算).

An introduction to the theory of quantum entanglement

Quantum entangled states play very important roles in quantum information processing, such as quantum teleportation, dense coding, error correction, cryptography, and computation. The theory of entanglement mainly concerns the characterization of quantum entanglement and the classification of quantum states, as well as its applications in quantum information processing. We present some basic concepts and results, including: the relationship between locality and reality in quantum mechanics and Bell inequalities, and that between Bell inequalities and the separability of quantum states; the definition of separability for pure and mixed quantum states, and some separability criteria such as the positive map approach, positive partial transpose, reduction criterion, realignment, entanglement witnesses, and the covariance matrix approach and local uncertainty relations; some entanglement measures such as the entanglement of formation, concurrence, relative entropy, negativity, tangle, entanglement of assistance, and their estimation; the change in entanglement when the physical system evolves or undergoes interaction with the environment.