How to construct entanglement witnesses

Abstract

We present very simple method for constructing indecomposable entanglement witnesses out of a given pair -- an entanglement witness W and the corresponding state detected by W. This method may be used to produce new classes of atomic witnesses which are able to detect the `weakest' quantum entanglement. Actually, it works perfectly in the multipartite case, too. Moreover, this method provides a powerful tool for constructing new examples of bound entangled states.

10 pages

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• When different entanglement witnesses detect entangled states simultaneously
• Spectral conditions for entanglement witnesses vs. bound entanglement
• A characterization of optimal entanglement witnesses
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• A class of exposed indecomposable positive maps
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• Necessary and sufficient criterion for k-separability of N-qubit noisy GHZ states
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• Entanglement witnesses for $d\otimes d$ systems and new classes of entangled qudit states
• Recurrent construction of optimal entanglement witnesses for 2N qubit systems
• Criteria and new classes of k-positive maps
• Tensor product extension of entanglement witnesses and their connection with measurement device independent entanglement
• Universal methods for extending any entanglement witness from the bipartite to the multipartite case
• Constructing positive maps from block matrices