Related papers: Optimal entanglement witnesses for two qutrits

We examine various notions related with the optimality for entanglement witnesses arising from Choi type positive linear maps. We found examples of optimal entanglement witnesses which are non-decomposable, but which are not…

We show that the entanglement witnesses based on local orthogonal observables which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005)] and [O. G\"uhne, M. Mechler, G. T\'oth and P. Adam, Phys. Rev. A 74, 010301…

We study the optimal entanglement witness with respect to multiqubits W-states. We show such entanglement witnesses can be used to distinguish genuine entangled states, different biseparable states and fully separable states.

In 2008, the conjecture that structural physical approximations to optimal entanglement witnesses are separable states (in general unnormalized) was posed. In an attempt to disprove it, in [K.-C. Ha and S.-H. Kye, Separable states with…

In this paper, we present a characterization of optimal entanglement witnesses in terms of positive maps and then provide a general method of checking optimality of entanglement witnesses. Applying it, we obtain new indecomposable optimal…

We provide two 1-parameter families of indecomposable entanglement witnesses in C4 {\otimes} C4. Following recent paper by Ha and Kye [Phys. Rev. A 84, 024302 (2011)] we show that these EWs are optimal and hence provide the strongest tool…

Recently, X. Qi and J. Hou [Phys. Rev. A 85, 022334 (2012)] provided optimal entanglement witnesses without the spanning property. These witnesses are associated to indecomposable positive linear maps, but it is not checked whether partial…

We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which…

A general formulation of the problem of detection for a pair of two cones is presented. The special case is the detection of entangled states by entanglement witnesses. Having defined what means "to detect", one can identify the subset of…

We interpret multi-partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them. We apply this result to multi-qubit {\sf X}-shaped Hermitian matrices, and characterize the conditions for them to be…

If one wants to establish optimality of a given bipartite entanglement witness, the current standard approach is to check whether it has the spanning property. Although this is not necessary for optimality, it is most often satisfied in…

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…

This paper is concerned with all tests for continuous-variable entanglement that arise from linear combinations of second moments or variances of canonical coordinates, as they are commonly used in experiments to detect entanglement. All…

Two approaches can be utilized to handle the separability problem, finding out whether a given bipartite qudit state is separable or not: a direct procedure on the state space or the effective tool of entanglement witnesses (EWs). This…

It is well known that the support of an optimal decomposable entanglement witness is completely entangled. We add two more necessary conditions for the optimality: The orthogonal complement of the support must have a nonzero product vector;…

We disprove the conjecture that structural physical approximations to optimal entanglement witnesses are separable states. The conjecture holds true for extremal decomposable entanglement witnesses.

We introduce informationally complete measurements whose outcomes are entanglement witnesses and so answer the question of how many witnesses need to be measured to decide whether an arbitrary state is entangled or not: as many as the…

We provide a new class of indecomposable entanglement witnesses. In 4 x 4 case it reproduces the well know Breuer-Hall witness. We prove that these new witnesses are optimal and atomic, i.e. they are able to detect the "weakest" quantum…

Linear and nonlinear entanglement witnesses for a given bipartite quantum systems are constructed. Using single particle feasible region, a way of constructing effective entanglement witnesses for bipartite systems is provided by exact…

How to detect quantum correlations in bi-partite scenarios using a split many-body system and collective measurements on each party? We address this question by deriving entanglement witnesses using either only first or first and second…