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A Characterization of Maximally Entangled Two-Qubit States

Authors:	Junjun Duan Lin Zhang Quan Qian Shao-Ming Fei

Institution:	1.School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China; (J.D.); (Q.Q.);2.Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany;3.School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Abstract:	As already known by Rana’s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval $- \frac{1}{2}, 1]$ . In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are $- \frac{1}{2}$ . For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is $- \frac{1}{2}$ 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.

Keywords:	maximally entangled state positive partial transpose moment