  For a quantum state in a bipartite system represented as a density matrix,
researchers used the realignment matrix and functions on its singular values to
study the separability of the quantum state. We obtain bounds for elementary
symmetric functions of singular values of realignment matrices. This answers
some open problems proposed by Lupo, Aniello, and Scardicchio. As a
consequence, we show that the proposed scheme by these authors for testing
separability would not work if the two subsystems of the bipartite system have
the same dimension.
