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

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• Norms and Cones in the Theory of Quantum Entanglement
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• Extremal extensions of entanglement witnesses and their connection with UPB
• Measurement-induced nonlocality over two-sided projective measurements
• Entanglement detection beyond the CCNR criterion for infinite-dimensions
• Symmetric measurement-induced lower bounds of concurrence
• Criteria and new classes of k-positive maps
• A class of generalized positive linear maps on matrix algebras
• The RCCN criterion of separability for states in infinite-dimensional quantum systems
• Criteria of positivity for linear maps constructed from permutation pairs
• Detection of entanglement via moments of positive maps
• Constructing positive maps from block matrices