A Characterization of Maximally Entangled Two-Qubit States - Junjun Duan; Lin Zhang; Quan Qian; Shao-Ming Fei (Entropy, 2022)
As already known by Rana’s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval <semantics>[−12,1]</semantics>. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are <semantics>−12</semantics>. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is <semantics>−12</semantics> 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.