Related papers: Entanglement witnesses with local partial ordering
The entanglement witness is an important and experimentally applicable tool for entanglement detection. In this paper, we provide a nonlinear improvement of any entanglement witness for $2\otimes d$ quantum systems. Compared with any…
The question under what conditions different witnesses may detect some entangled states simultaneously is answered for both finite- and infinite-dimensional bipartite systems. Finite many different witnesses can detect some entangled states…
We construct three-qubit entanglement witnesses with the properties that all the partial transposes have the spanning properties. These witnesses determine faces for separable states whose interior lies in the interior of PPT states, and so…
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…
We provide a systematic method for nonlinear entanglement detection based on trace polynomial inequalities. In particular, this allows to employ multi-partite witnesses for the detection of bipartite states, and vice versa. We identify…
In 2017 an idea considering a pair of Hermitian operators of product form was published, which is called ultrafine entanglement witnessing. In 2018 some rigorous results were given. Here we improve their work. First we point this idea can…
Entanglement detection is one of the important problems in quantum information theory. To deal with this problem, many entanglement detection criteria have been proposed. Among the proposed criteria, the detection of entanglement through…
We study extremal entanglement witnesses on a bipartite quantum system. We define the cone of witnesses as the dual of the set of separable density matrices, thus $\textrm{Tr}\,\Omega\rho\geq 0$ when $\Omega$ is a witness and $\rho$ a pure…
We consider multipartite quantum state discrimination and provide a specific relation between the properties of entanglement witness and quantum nonlocality inherent in the confidence of measurements. We first provide the definition of the…
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…
The separability problem is formulated in terms of a characterization of a single entanglement witness. More specifically, we show that any (in general multipartite) state \varrho is separable if and only if a specially constructed…
In this paper we address the problem of detection of entanglement using only few local measurements when some knowledge about the state is given. The idea is based on an optimized decomposition of witness operators into local operators. We…
We analyze the recently introduced notion of quantumness witness and compare it to that of entanglement witness. We show that any entanglement witness is also a quantumness witness. We then consider some physically relevant examples and…
We present the experimental detection of genuine multipartite entanglement using entanglement witness operators. To this aim we introduce a canonical way of constructing and decomposing witness operators so that they can be directly…
We show that any state which violates the computable cross norm (or realignment) criterion for separability also violates the separability criterion of the local uncertainty relations. The converse is not true. The local uncertainty…
We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…
We introduce a new kind of Entanglement Witness which is appropriate for studying genuine multipartite entanglement in large systems. The witness operator has a form that fits naturally to quantum states represented by tensor networks. It…
Quantum entanglement lies at the heart of quantum mechanics and quantum information processing. In this work, we show a new framework where entangled states play the role of witnesses. We extend the notion of entanglement witnesses,…
We present an unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the concurrence and the robustness of…
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…