Related papers: Graphs States and the necessity of Euler Decomposi…

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…

Any 8-qubit graph state belongs to one of the 101 equivalence classes under local unitary operations within the Clifford group. For each of these classes we obtain a representative which requires the minimum number of controlled-Z gates for…

Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…

We exactly evaluate a number of multipartite entanglement measures for a class of graph states, including d-dimensional cluster states (d = 1,2,3), the Greenberger-Horne-Zeilinger states, and some related mixed states. The entanglement…

Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently complex network theory has been applied to quantum systems, where complex…

Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…

We develop a heuristic graph coloring approximation algorithm that uses the D-Wave 2X as an independent set sampler and evaluate its performance against a fully classical implementation. A randomly generated set of small but hard graph…

There is a famous problem in geometric graph theory to find the chromatic number of the unit distance graph on Euclidean space; it remains unsolved. A theorem of Erdos and De-Bruijn simplifies this problem to finding the maximum chromatic…

Strong nonlocality based on local distinguishability is a stronger form of quantum nonlocality recently introduced in multipartite quantum systems: an orthogonal set of multipartite quantum states is said to be of strong nonlocality if it…

We show how graph theory concepts can provide an insight into the origin of slow dynamics in systems with kinetic constraints. In particular, we observe that slow dynamics is related to the presence of strong hierarchies between nodes on…

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…

Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a…

Tensor models and, more generally, group field theories are candidates for higher-dimensional quantum gravity, just as matrix models are in the 2d setting. With the recent advent of a 1/N-expansion for coloured tensor models, more focus has…

There has been a great deal of attention recently to graphs whose vertex set is a group, defined using the group structure. (The commuting graph, where two elements are joined if they commute, is the oldest and most famous example.) The…

We introduce a graph theoretic property called Condition (N) for finitely separated graphs and prove that it is equivalent to both nuclearity and exactness of the associated universal tame graph C*-algebra.

We discuss high energy properties of states for (possibly interacting) quantum fields in curved spacetimes. In particular, if the spacetime is real analytic, we show that an analogue of the timelike tube theorem and the Reeh-Schlieder…

For each commutative, graded algebra with finite dimension in each degree, we construct a graded cohomology theory for graphs whose graded Euler characteristic is the chromatic polynomial of the graph. This extends our previous work which…

We use the concept of \textit{entangled graphs} with weighted edges to present a classification for four-qubit entanglement which is based neither on the LOCC nor the SLOCC. Entangled graphs, first introduced by Plesch et al. [Phys. Rev. A…

We analyze composed quantum systems consisting of $k$ subsystems, each described by states in the $n$-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual…