相关论文: Entangled Graphs

The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum information theory. Here, we completely characterize genuine multiparticle entanglement for…

We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is…

Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we…

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map Phi which operates on state spaces with even dimension N >= 4. It is shown that Phi detects many entangled states…

We present a method to quantify entanglement in mixed states of highly symmetric systems. Symmetry constrains interactions between parts and predicts the degeneracies of the states. While symmetry alone produces entangled eigenstates, the…

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…

We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…

We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and…

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so…

We exactly evaluate the entanglement of a six vertex and a nine vertex graph states which correspond to non ''two-colorable'' graphs. The upper bound of entanglement for five vertices ring graph state is improved to 2.9275, less than upper…

We review the problem of discriminating entangled states from separable states for bipartite systems. We formally define what entangled states are, present some important criteria to detect entanglement, and show how they can be classified…

We investigate a family of quantum states defined by directed graphs, where the oriented edges represent interactions between ordered qubits. As a measure of entanglement, we adopt the Entanglement Distance - a quantity derived from the…

We propose the definition of the geometric measure of entanglement for continuous variable states. On the basis of this definition we examine entanglement of the graph states obtained as a result of action of a unitary operator on the…

We address the question of quantifying entanglement in pure graph states. Evaluation of multipartite entanglement measures is extremely hard for most pure quantum states. In this paper we demonstrate how solving one problem in graph theory,…

We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-Z gates. We study the entanglement features of…

A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner…

Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying…

Using the signed laplacian matrix, and weighted and hybrid graphs, we present additional ways to interpret graphs as grid states. Hybrid graphs offer the most general interpretation. Existing graphical methods that characterize entanglement…

We present new combinatorial objects, which we call grid-labelled graphs, and show how these can be used to represent the quantum states arising in a scenario which we refer to as the faulty emitter scenario: we have a machine designed to…

We give a new separability criterion, a necessary condition for separability of $N$-partite quantum states. The criterion is based on the Bloch representation of a $N$-partite quantum state and makes use of multilinear algebra, in…