量子信道对广义纠缠鲁棒性的影响

The influences of quantum channels on the generalized robustness of entanglement

根据量子态之集是一个凸闭集,证明了广义纠缠鲁棒性定义中的下确界是可以取到的,说明了同一量子态的两个广义最优态的凸组合仍是广义最优态,广义纠缠鲁棒性作为定义态集合上函数是下半连续的。其次,分别给出了一个量子信道不增加(不减少、保持)所有量子态的广义纠缠鲁棒性的充分必要条件。最后,作为应用得到了相关已有结果。

Based on the fact that the set of all separable states is a convex-closed set,it is proved that the infimum in the definition of the generalized robustness of entanglement( GRo E) can be attained; second,it is illustrated that a convex combination of tw o generalized optimal states of a state is still a generalized optimal state and the GRo E is a lower semicontinuous function on the set of all quantum states of a mult-partite system; lastly,necessary and sufficient conditions for a quantum channel to decrease( resp. increase,maintain) the GRo E of all quantum states were obtained. Final,as applications,some existing results were derived.