In this paper,we discuss the relationship among quantum mutual information,geometry quantum discord and weak geometry quantum discord based on the weak measurement,and propose a class of necessary and sufficient conditions for product states in the bipartite quantum systems.%探讨了两体量子系统量子互信息、几何量子失协和弱几何量子失协之间的关系,并给出了两体量子系统上一个量子态为乘积态的一类充分必要条件.
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