Related papers: Witnessing and guiding sets of tangles

Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby discover, relate, and structure types: of behaviour,…

Entanglement witnesses are observables which when measured, detect entanglement in a measured composed system. It is shown what kind of relations between eigenvectors of an observable should be fulfilled, to allow an observable to be an…

Tangles, as introduced by Robertson and Seymour, were designed as an indirect way of capturing clusters in graphs and matroids. They have since been shown to capture clusters in much broader discrete structures too. But not all tangles are…

Originally, tangles were invented as an abstract tool in mathematical graph theory to prove the famous graph minor theorem. In this paper, we showcase the practical potential of tangles in machine learning applications. Given a collection…

We establish a connection between tangles, a concept from structural graph theory that plays a central role in Robertson and Seymour's graph minor project, and hierarchical clustering. Tangles cannot only be defined for graphs, but in fact…

Using the new framework of graph separations developed recently by Diestel and Oum, we show that there is a natural witness to large branch-width which can be defined in a similar way to a bramble. We also apply our methods to a more recent…

Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically…

We investigate a class of entanglement witnesses where each witness is formulated as a difference of two product observables. These observables are decomposable into positive semidefinite local operators that obey a partial ordering rule…

Entanglement witnesses are invaluable for efficient quantum entanglement certification without the need for expensive quantum state tomography. Yet, standard entanglement witnessing requires multiple measurements and its bounds can be…

Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby identify and discover 'types': of behaviour, views,…

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in…

We give a universal recipe for constructing nonlinear entanglement witnesses able to detect non-classical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The…

By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…

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 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 construct both nonlinear and linear entanglement witnesses, by tensoring and partial tracing existing states and witnesses. We show that little shared quantum resources allow to employ decomposable witnesses to obtain larger ones…

Quantitative entanglement witnesses allow one to bound the entanglement present in a system by acquiring a single expectation value. In this paper we analyze a special class of such observables which are associated with (generalized) Werner…

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the…

An entanglement witness is an observable with the property that a negative expectation value signals the presence of entanglement. The question arises how a witness can be improved if the expectation value of a second observable is known,…

From the physical point of view entanglement witnesses define a universal tool for analysis and classification of quantum entangled states. From the mathematical point of view they provide highly nontrivial generalization of positive…