Class Of Positive Maps Research Articles

A class of optimal positive maps in Mn

It is proven that a certain class of positive maps in the matrix algebra Mn consists of optimal maps, i.e. maps from which one cannot subtract any completely positive map without loosing positivity. This class provides a generalization of a seminal Choi positive map in M3.

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.

On Kossakowski Construction of Positive Maps on Matrix Algebras

We provide the continuation of an analysis of a class of positive maps proposed ten years ago by Kossakowski. In particular, we propose a new parametrization which reveals an elegant geometric structure and an interesting interplay between group theory and a certain class of positive maps.

Geometry of quantum states: New construction of positive maps

We provide a new class of positive maps in matrix algebras. The construction is based on the family of balls living in the space of density matrices of n-level quantum system. This class generalizes the celebrated Choi map and provide a wide family of entanglement witnesses which define a basic tool for analyzing quantum entanglement.