Related papers: Conditions for separability in generalized Laplaci…
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 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…
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…
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…
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…
The Peres-Horodecki criterion of positivity under partial transpose is studied in the context of separability of bipartite continuous variable states. The partial transpose operation admits, in the continuous case, a geometric…
The density matrix of a graph is the combinatorial laplacian matrix of a graph normalized to have unit trace. In this paper we generalize the entanglement properties of mixed density matrices from combinatorial laplacian matrices of graphs…
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…
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices. We give some basic properties and…
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…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
We give necessary and sufficient conditions under which a density matrix acting on a two-fold tensor product space is separable. Our conditions are given in terms of quantum conditional information transmission.
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…
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…
We consider nonnegative r-potent matrices with finite dimensions and study their decomposability. We derive the precise conditions under which an r-potent matrix is decomposable. We further determine a general structure for the r-potent…
Explicit separable density matrices, for mixed two qubits states, are derived by the use of Hilbert Schmidt decompositions and Peres Horodecki criterion. A strongly separable two qubits mixed state is defined by multiplications of two…
In a series of papers with Kossakowski, the first author has examined properties of densities for which the positive partial transpositrionm (PPT) property can be readily checked. These densities were also investigated from a different…
The question of when zeros (i.e., sparsity) in a positive definite matrix $A$ are preserved in its Cholesky decomposition, and vice versa, was addressed by Paulsen et al. in the Journal of Functional Analysis (85, pp151-178). In particular,…
A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…
The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is…