Positive finite rank elementary operators and characterizing entanglement of states
Xiaofei Qi, Jinchuan Hou · Journal of Physics A Mathematical and Theoretical · 2011
In this paper, some indecomposable positive finite rank elementary operators of order ( n , n ) are constructed. This allows us to give a simple necessary and sufficient criterion for the separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order (2, 2) and obtain some new mixed entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion.