中文摘要：

围绕判断一个两体量子态是否纠缠的问题（量子态的可分离判据问题）,寻求能够解决该问题的全新论据或重要结论.利用矩阵分析和线性代数的纯数学分析,得到了可分离态的一些性质和一些特殊情况下的纠缠判据,并重点探讨了2×N和N×2维量子态这一特殊情况.

英文摘要：

The separability problem in quantum information theory was discussed and new separability criteria was searched for in order to tell whether a given quantum state is separable or entangled.Some properties of separable states as well as some separability criteria for special cases were obtained,and our discussion was focused on quantum states in a Hilbert space of 2×N or N×2.