A class of positive atomic maps

Abstract

We construct a new class of positive indecomposable maps in the algebra of `d x d' complex matrices. These maps are characterized by the `weakest' positivity property and for this reason they are called atomic. This class provides a new reach family of atomic entanglement witnesses which define important tool for investigating quantum entanglement. It turns out that they are able to detect states with the `weakest' quantum entanglement.

15 pages

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• How to construct entanglement witnesses
• Constructing optimal entanglement witnesses. II
• Optimal entanglement witnesses from generalized reduction and Robertson maps
• A class of exposed indecomposable positive maps
• Exposed positive maps in M_4(C)
• Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps
• Entanglement witnesses for $d\otimes d$ systems and new classes of entangled qudit states
• A class of generalized positive linear maps on matrix algebras
• Tensor product extension of entanglement witnesses and their connection with measurement device independent entanglement
• On classical and quantum liftings