Related papers: Positive maps, states, entanglement and all that; …

We introduce a 3-parameter class of maps acting on a bipartite system that are a natural generalisation of the depolarizing channel (and include it as a special case). Then, we find the exact regions of the parameter space that…

We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with…

The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…

We propose a family of positive maps constructed from a recently introduced class of symmetric measurements. These maps are used to define entanglement witnesses, which include other popular approaches with mutually unbiased bases and…

In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…

For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…

We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear…

New types of magnetic structures in the Heisenberg model are found. Analytical methods are used to describe spiral structures, spiral vortex structures, and their interaction. Methods for obtaining these structures in real systems,…

We present two different descriptions of positive partially transposed (PPT) states. One is based on the theory of positive maps while the second description provides a characterization of PPT states in terms of Hilbert space vectors. Our…

We study equivariant linear maps between finite-dimensional matrix algebras, as introduced by Bhat. These maps satisfy an algebraic property which makes it easy to study their positivity or k-positivity. They are therefore particularly…

We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete…

We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…

We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 x 3 complex matrices. It turns out that boundary of this set…

We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way,…

We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…

By the Choi matrix criteria it is easy to determine if a specific linear matrix map is completely positive, but to establish whether a linear matrix map is positive is much less straightforward. In this paper we consider classes of linear…

A linear map between real symmetric matrix spaces is positive if all positive semidefinite matrices are mapped to positive semidefinite ones. A real symmetric matrix is separable if it can be written as a summation of Kronecker products of…

We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…

Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…

The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear…