Positive finite rank elementary operators and characterizing entanglement of states

Abstract

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.

26 pages

References in corpus (3)

• Detecting Genuine Multipartite Entanglement with Two Local Measurements
• A characterization of positive linear maps and criteria of entanglement for quantum states
• Constructing entanglement witnesses for infinite-dimensional systems

Cited by in corpus (2)

• Lower Bound of Concurrence Based on Positive Maps
• The RCCN criterion of separability for states in infinite-dimensional quantum systems