Positive finite rank elementary operators and characterizing entanglement of states

الأصل · EN

In this paper, a class of indecomposable positive finite rank elementary operators of order (n,n) are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order (2,2) and get some new mixed entangled states that can not be detected by the positive partial transpose (PPT) criterion and the realignment criterion.