Related papers: Entangled Graphs

We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this…

It is shown that local distinguishability of orthogonal mixed states can be completely characterized by local distinguishability of their supports irrespective of entanglement and mixedness of the states. This leads to two kinds of upper…

Bound entangled states are states that are entangled but from which no entanglement can be distilled if all parties are allowed only local operations and classical communication. However, in creating these states one needs nonzero…

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states.…

We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We…

In this paper, a theorem is proved that generalizes several existing amalgamation results in various ways. The main aim is to disentangle a given edge-colored amalgamated graph so that the result is a graph in which the edges are shared out…

It is shown that for a constant $t\in \mathbb{N}$, every simple topological graph on $n$ vertices has $O(n)$ edges if it has no two sets of $t$ edges such that every edge in one set is disjoint from all edges of the other set (i.e., the…

The geometric measure of entanglement of a pure state, defined by its distance to the set of pure separable states, is extended to multipartite mixed states. We characterize the nearest disentangled mixed state to a given mixed state with…

In this Letter we present a new quantity that shows whether two general qubit systems are entangled, which we call harmony. It captures the notion of separability and maximal entanglement. It is also shown that harmony is monogamous for…

While finite graphs have tree-decompositions that efficiently distinguish all their tangles, locally finite graphs with thick ends need not have such tree-decompositions. We show that every locally finite graph without thick ends admits…

We show that if a graph contains few induced copies of a given graph then its edges are distribited unevenly.

We review the theory of multi-particle entanglement. In this book chapter we aim at briefly ``setting the coordinates'' and guiding through the extensive literature in this field. Our coordinate system chosen for this chapter has the axes…

The indistinguishability of quantum particles is widely used as a resource for the generation of entanglement. Linear quantum networks (LQNs), in which identical particles linearly evolve to arrive at multimode detectors, exploit the…

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the…

The state of an entangled q-bit pair is specified by 15 numerical parameters that are naturally regarded as the components of two 3-vectors and a $3\times3$-dyadic. There are easy-to-use criteria to check whether a given pair of 3-vectors…

For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the…

The study on the entanglement polygon inequality of multipartite systems has attracted much attention. However, most of the results are on pure states. Here we consider the property for a class of mixed states, which are the reduced density…

We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…

We present a large class of indecomposable exposed positive linear maps between three dimensional matrix algebras. We also construct two qutrit separable states with lengths ten in the interior of their dual faces. With these examples, we…

The class of entangled $N$-qubit states known as graph states, and the corresponding stabilizer groups of $N$-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum…