Interpolating between Positive and Completely Positive Maps: A New Hierarchy of Entangled States

A new class of positive maps is introduced. It interpolates between positive and completely positive maps. It is shown that this class gives rise to a new characterization of entangled states. Additionally, it provides a refinement of the well-known classes of entangled states characterized in terms of the Schmidt number. The analysis is illustrated with examples of qubit maps.