相关论文: Abstract Operator Systems over the Cone of Positiv…

We transfer the theory of slack operators and sums-of-squares-criteria for lifts from convex cones to operator systems. These allow to study the following question, among others: Given an abstract operator system, is its enveloping…

We study dynamical semigroups of positive, but not completely positive maps on finite-dimensional bipartite systems and analyze properties of their generators in relation to non-decomposability and bound-entanglement. An example of…

Convex sets of completely positive maps and positive semidefinite kernels are considered in the most general context of modules over $C^*$-algebras and a complete charaterization of their extreme points is obtained. As a byproduct, we…

We determine the structure of all bijections on the cone of positive semidefinite operators which preserve the quantum $f$-divergence for an arbitrary strictly convex function $f$ defined on the positive halfline. It turns out that any such…

We systematically study how properties of abstract operator systems help classifying linear matrix inequality definitions of sets. Our main focus is on polyhedral cones, the 3-dimensional Lorentz cone, where we can completely describe all…

We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…

We use a new idea that emerged in the examination of exposed positive maps between matrix algebras to investigate in more detail the difference between positive maps on $M_2(C)$ and $M_3(C)$. Our main tool stems from classical Grothendieck…

The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…

We examine k-minimal and k-maximal operator spaces and operator systems, and investigate their relationships with the separability problem in quantum information theory. We show that the matrix norms that define the k-minimal operator…

The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one hand we confirm that the classification problems for…

We initiate a study of linear maps on $M_n(\mathbb{C})$ that have the property that they factor through a tracial von Neumann algebra $(\mathcal{A,\tau})$ via operators $Z\in M_n(\mathcal{A})$ whose entries consist of positive elements from…

We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The…

This paper considers two frequently used matrix representations -- what we call the $\chi$- and $\mathcal{S}$-matrices -- of a quantum operation and their applications. The matrices defined with respect to an arbitrary operator basis, that…

We provide a partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions. This construction generalizes celebrated Choi example of a map which is positive but not completely positive.…

Given an Archimedean order unit space (V,V^+,e), we construct a minimal operator system OMIN(V) and a maximal operator system OMAX(V), which are the analogues of the minimal and maximal operator spaces of a normed space. We develop some of…

The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the density…

We establish explicit means via which natural dilations of completely positive (CP) maps can be constructed \`a la Kraus's IInd representation theorem. To obtain this, we rely on the Choi-Jamio{\l}kowski correspondence and develop a…

In this article we consider means of positive operators on a Hilbert space. We extend the theory of matrix power means to arbitrary operator means in the sense of Kubo-Ando. The basis of the extension is relying on ideas coming from…

Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…

Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a…