A class of positive atomic maps

We construct a new class of positive indecomposable maps in the algebra of d × 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 rich family of atomic entanglement witnesses which define an important tool for investigating quantum entanglement. It turns out that they are able to detect states with the 'weakest' quantum entanglement.

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