Related papers: Entanglement detection with trace polynomials

We introduce two entanglement conditions that take the form of inequalities involving expectation values of operators. These conditions are sufficient conditions for entanglement, that is if they are satisfied the state is entangled, but if…

It is shown that, every entangled state in an infinite-dimensional composite system has a simple entanglement witness of the form $\alpha I+T$ with $\alpha$ a nonnegative number and $T$ a finite rank self-adjoint operator. We also provide…

We propose a family of entanglement witnesses and corresponding positive maps that are not completely positive based on local orthogonal observables. As applications the entanglement witness of the $3\times 3$ bound entangled state [P.…

We derive a set of algebraic equations, the so-called multipartite separability eigenvalue equations. Based on their solutions, we introduce a universal method for the construction of multipartite entanglement witnesses. We witness…

Random local measurements have recently been proposed to construct entanglement witnesses and thereby detect the presence of bipartite entanglement. We experimentally demonstrate the efficacy of one such scheme on a two-qubit NMR quantum…

We consider entanglement witnesses arising from positive linear maps which generate exposed extremal rays. We show that every entanglement can be detected by one of these witnesses, and this witness detects a unique set of entanglement…

Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the…

Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of…

We present several criteria for genuine multipartite entanglement from universal uncertainty relations based on majorization theory. Under non-negative Schur-concave functions, the vector-type uncertainty relation generates a family of…

We present a development of a geometric approach to entanglement indicators. The method is applied to detect genuine multiqubit entanglement. The criteria are given in form of non-linear conditions imposed on correlation tensors. Thus they…

We propose a scheme for witnessing entanglement in phase space by significantly inefficient detectors. The implementation of this scheme does not require any additional process for correcting errors in contrast to previous proposals.…

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an…

Entanglement detection is one of the most conventional tasks in quantum information processing. While most experimental demonstrations of high-dimensional entanglement rely on fidelity-based witnesses, these are powerless to detect…

We give an introduction to Gaussian states and operations. A discussion of the entanglement properties of bipartite Gaussian states in terms of its covariance matrix follows. It is explained how entanglement can be witnessed using feasible…

Entanglement witnesses (EWs) are a fundamental tool for the detection of entanglement. We investigate the inertias of bipartite EWs constructed by the partial transpose of NPT states. Furthermore, we find out most of the inertias of the…

We formulate some properties of a set of several mutually unbiased measurements. These properties are used for deriving entropic uncertainty relations. Applications of mutually unbiased measurements in entanglement detection are also…

The variety of multi-partite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view classifications have been introduced.…

We derive a general criterion to detect entangled states in multi-partite systems based on the symmetric logarithmic derivative quantum Fisher information. This criterion is a direct consequence of the fact that separable states do not…

We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons and fermions. In each case properties of an entanglement measures are related to the decomposition of the suitably chosen representation of the…

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…