Related papers: Separable states and positive maps

The concurrence vectors are proposed by employing the fundamental representation of $A_n$ Lie algebra, which provides a clear criterion to evaluate the entanglement of bipartite system of arbitrary dimension for both pure and mixed states.…

Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…

This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…

In the present paper we study the structure of C^*-algebras generated by the components of the polar decompositions of operators in Hilbert space satisfying certain commutation relations.

Diagrammatic representation and manipulation of tensor networks has proven to be a useful tool in mathematics, physics, and computer science. Here we present several important and mostly well-known theorems regarding the dualities between…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

Let H(1), H(2) be complex Hilbert spaces, H be their Hilbert tensor product and let tr2 be the operator of taking the partial trace of trace class operators in H with respect to the space H(2). The operation tr2 maps states in H (i.e.…

In early days of quantum theory it was believed that the results of measurements performed on two distant physical systems should be uncorrelated thus their quantum state should be separable it means described by a simple tensor product of…

A linear relation, i.e., a multivalued operator $T$ from a Hilbert space ${\mathfrak H}$ to a Hilbert space ${\mathfrak K}$ has Lebesgue type decompositions $T=T_{1}+T_{2}$, where $T_{1}$ is a closable operator and $T_{2}$ is an operator or…

We consider two systems of harmonically trapped particles in a typical pure state of the Hilbert space defined by given values of the particle numbers and energies of the two gases. Such a state is entangled but we show that, for large…

In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied…

We study extensions of the mappings arising in usual channel-state duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with…

We recover the rays in the tensor product of Hilbert spaces within a larger class of so called `states of compoundness', structured as a complete lattice with the `state of separation' as its top element. At the base of the construction…

One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a…

We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically…

In this work, generalizations of some inequalities for continuous $h$-synchronous ($h$-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.

This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…

Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over…

We propose a measure of state entanglement for states of the tensor-product of C*-algebras.

Abelian duality is realized naturally by combining differential cohomology and locally covariant quantum field theory. This leads to a C$^*$-algebra of observables, which encompasses the simultaneous discretization of both magnetic and…