Interpolating between positive and completely positive maps: a new hierarchy of entangled states

TL;DR

The paper introduces a new class of positive maps that interpolate between positive and completely positive maps, offering a refined characterization of entangled states and their Schmidt number, with illustrative qubit examples.

Contribution

It presents a novel class of positive maps that bridges existing categories and enhances the understanding of entangled states and Schmidt number classifications.

Findings

New class of positive maps interpolates existing categories.

Provides a refined characterization of entangled states.

Illustrated with examples of qubit maps.

Abstract

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 term of the Schmidt number. The analysis is illustrated with examples of qubit maps.