A Characterization of Maximally Entangled Two-Qubit States

As already known by Rana’s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval [Formula: see text]. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are [Formula: see text]. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is [Formula: see text] if and only if such a two-qubit state is maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.