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In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.doi:10.1007/s11434-013-5738-x fatcat:6j74x3ic3ja3ffzvh7obyqh6cy