Related papers: Separable states and positive maps

This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties…

We analyze semigroups of decomposable maps on C*-algebras in context of the algebraic structure of associated infinitesimal generators. Case of von Neumann algebras, including $B(\mathcal{H})$ for $\mathcal{H}$ a Hilbert space, is also…

We introduce a nessecary condition for a state to be separable and apply this condition to the SPA of an optimal ositive map and give a proof of the fact that the SPA need not be the density ooperator for a separable state.

Using pure entangled Schmidt states, we show that m-positivity of a map is bounded by the ranks of its negative Kraus matrices. We also give an algebraic condition for a map to be m-positive. We interpret these results in the context of…

We define and systematically study nonassociative C*-algebras as C*-algebras internal to a topological tensor category. We also offer a concrete approach to these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded operators…

We study actions of countable discrete amenable groups on unital separable simple nuclear Z-absorbing C*-algebras. Under a certain assumption on tracial states, which is automatically satisfied in the case of a unique tracial state, the…

Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a class of indecomposable positive maps in the algebra of 2n x 2n complex matrices with n>1. It is shown that these maps are exposed and hence…

We show that the pure state evaluation map from $ M_{n}(\mathbb{C}) $ to $ C(\mathbb{C} \mathbb{P}^{n-1}) $ (a completely positive map of $ C^{*} $-algebras) extends to a cochain map from the universal calculus on $ M_{n}(\mathbb{C} ) $ to…

Consider two non-degenerate algebras B and C over the complex numbers. We study a certain class of idempotent elements E in the multiplier algebra of the tensor product of B with C, called separability idempotents. The conditions include…

In this paper we consider power means of positive Hilbert space operators both in the conventional and in the Kubo-Ando senses. We describe the corresponding isomorphisms (bijective transformations respecting those means as binary…

We introduce a generalization of the set of completely positive matrices that we call "pairwise completely positive" (PCP) matrices. These are pairs of matrices that share a joint decomposition so that one of them is necessarily positive…

Entanglement of states and Complete Positivity of maps are concepts that have achieved physical importance with the recent growth of quantum information science. They are however mathematically relevant whenever tensor products of complex…

We reflect on the notions of positivity and square roots. We review many examples which underline our thesis that square roots of positive maps related to *-algebras are Hilbert modules. As a result of our considerations we discuss…

We give necessary and sufficient conditions under which a density matrix acting on a two-fold tensor product space is separable. Our conditions are given in terms of quantum conditional information transmission.

Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful…

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. This is a brief review in which we consider the problem for states in infinite dimensional Hilbert spaces.…

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 positive maps. In particular, the equivalence…

Substantial progress has recently been reported in the determination of the Hilbert-Schmidt (HS) separability probabilities for two-qubit and qubit-qutrit (real, complex and quaternionic) systems. An important theoretical concept employed…

In this paper we study the operator inequality \phi(X)\leq X and the operator equation \phi(X)= X, where \phi is a w^*-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one…

I introduce yet another way to associate a C*-algebra to a graph and construct a simple nuclear C*-algebra that has irreducible representations both on a separable and a nonseparable Hilbert space.