Related papers: The tripartite separability of density matrices of…
We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that…
We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree…
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…
Density matrices of graphs are combinatorial laplacians normalized to have trace one (Braunstein \emph{et al.} \emph{Phys. Rev. A,} \textbf{73}:1, 012320 (2006)). If the vertices of a graph are arranged as an array, then its density matrix…
A new layers method is presented for multipartite separability of density matrices from simple graphs. Full separability of tripartite states is studied for graphs on degree symmetric premise. The models are generalized to multipartite…
Normalized Laplacian matrices of graphs have recently been studied in the context of quantum mechanics as density matrices of quantum systems. Of particular interest is the relationship between quantum physical properties of the density…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum…
In this paper we prove a separability criterion for mixed states in $\mathbb C^p\otimes\mathbb C^q$. We also show that the density matrix of a graph with only one entangled edge is entangled.
In this paper we give the new sufficient conditions of entanglement for multipartite qubit density matrixes. We discuss in detail the case for tripartite qubit density matrixes. As a criterion in concrete application, its steps are quite…
In this Letter we find the new criteria of separability of multipartite qubit density matrixes. Especially, we discuss in detail the criteria of separability for tripartite qubit density matrixes. We find the sufficient and necessary…
Braunstein et. al. have started the study of entanglement properties of the quantum states through graph theoretical approach. Their idea was to start from a simple unweighted graph $G$ and then they have defined the quantum state from the…
Recently, Laplacian matrices of graphs are studied as density matrices in quantum mechanics. We continue this study and give conditions for separability of generalized Laplacian matrices of weighted graphs with unit trace. In particular, we…
We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The conjecture states…
Representing graphs as quantum states is becoming an increasingly important approach to study entanglement of mixed states, alternate to the standard linear algebraic density matrix-based approach of study. In this paper, we propose a…
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 determine the minimal density of triangles in a tripartite graph with prescribed edge densities. This extends a previous result of Bondy, Shen, Thomass\'e and Thomassen characterizing those edge densities guaranteeing the existence of a…
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit…
This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the…
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…