SOT-不可分离Witness的比较

Comparation of SOT-Inseparability Witnesses

在可分无限维复Hilbert张量积空间上,每个SOT-不可分离正算子都能用某个SOT-不可分离witness来检测。通过讨论不同SOT-不可分离Witness的比较问题,分别给出它们可以比较、等价、最优、能同时检测某SOT-不可分离正算子以及不能同时检测任何SOT-不可分离正算子的充分必要条件。

On a tensor product of separable complex Hilbert space,every SOT-inseparable positive operator can be detected by an SOT-inseparability witness.In this paper,the relations of different SOT-inseparability witnesses is discussed.The necessary and sufficient conditions are given for two witnesses to be comparable,to be equivalent,to be optimal,to detect some common SOT-inseparable positive operators,and to detect no common SOT-inseparable positive operators,respectively.