Abstract: We first investigated the perfect discrimination of mixed quantum, and analyzed the local discrimination of quantum orthogonal mixed states using the Schmidt number of the states, gaining two necessary conditions. One is that quantum orthogonal mixed states for discrimination must be product states; on the base of the results, we also proved that two arbitrary bipartite orthogonal product states can be distinguished by local operation and classical communication (LOCC). The other is that the sum of the Schmidt numbers of the mixed states should be less than the dimension of the whole Hilbert space which the states belong to. 

Key words: orthogonal mixed states, entanglement, local operation and classical communication discrimination, Schmidt number