  We give necessary conditions for the mixing problem in bipartite case, which
are independent of eigenvalues and based on algebraic-geometric invariants of
the bipartite states. One implication of our results is that for some special
bipartite mixed states, only special mixed states in a measure zero set can be
used to mix to get them. The results indicate for many physical problems on
composite quantum systems the description based on majorization of eigenvalues
is not sufficient
