An alternative, geometrical proof of a known theorem concerning the decomposition of
positive maps of the matrix algebra $ M_ {2}(\mathbb {C}) $ has been presented. The …

Drawing on results of Choi, Størmer and Woronowicz, we present a nearly complete
characterization of certain important classes of positive maps. In particular, we construct a …

We provide partial classification of positive linear maps in matrix algebras which is based on
a family of spectral conditions. This construction generalizes the celebrated Choi example of …

Let Φ be a trace-preserving, positivity-preserving (but not necessarily completely positive)
linear map on the algebra of complex 2× 2 matrices, and let Ω be any finite-dimensional …

Let K be a convex subset of the state space of a finite-dimensional C*-algebra. We study the
properties of channels on K, which are defined as affine maps from K into the state space of …

We analyze positivity of a tensor product of two linear qubit maps, ${{\Phi} _ {1}}\otimes
{{\Phi} _ {2}} $. Positivity of maps ${{\Phi} _ {1}} $ and ${{\Phi} _ {2}} $ is a necessary but not a …

Motived by the importance of quantum operations in quantum information theory, we
rigorously present the three equivalent (Stinespring, Kraus, and Choi) forms of completely …

The structure of cones of positive and k-positive maps acting on a finite-dimensional Hilbert
space is investigated. Special emphasis is given to their duality relations to the sets of …

We outline a new approach to the characterization as well as to the classification of positive
maps. This approach is based on the facial structures of the set of states and of the cone of …

A family of linear positive maps in the algebra of 3× 3 complex matrices proposed recently
by Bera et al.(Linear and Multilinear Algebra, 2024) is further analyzed. It provides a …