On the origin of non-decomposable maps

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.

Incorrect example given in subsection 5.5 was removed

References in corpus (4)

• Optimal entanglement criterion for mixed quantum states
• Radon-Nikodym derivatives of quantum operations
• On non-completely positive quantum dynamical maps on spin chains
• On positive maps in quantum information