# On the origin of non-decomposable maps

## TL;DR

This paper uses the Radon-Nikodym formalism to analyze positive maps on finite-dimensional operator algebras, providing criteria and a method to construct non-decomposable maps crucial for quantum information theory.

## Contribution

It introduces a novel application of the Radon-Nikodym formalism to characterize and construct non-decomposable positive maps in finite dimensions.

## Key findings

- Criteria for non-decomposability of positive maps
- A new recipe for constructing non-decomposable maps
- Enhanced understanding of positive map structure in quantum theory

## Abstract

The Radon-Nikodym formalism is used to study the structure of the set of positive maps from $\mathcal{B}(\mathcal{H})$ into itself, where $\mathcal{H}$ is a finite dimensional Hilbert space. In particular, this formalism was employed to formulate simple criteria which ensure that certain maps are non decomposable. In that way, a recipe for construction of non decomposable maps was obtained.