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We clarify the microscopic structure of the entangling quantum measurement superoperators and examine their possible physical realization in a simple three-qubit model, which implements the entangling quantum measurement with an arbitrary…
We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$-qubit pure states (PRA \textbf{77}, 062334…
Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are only available in few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition…
Measuring entanglement is a demanding task in the field of quantum computation and quantum information theory. Recently, some authors experimentally demonstrated an embedding quantum simulator, using it to efficiently measure two-qubit…
Entanglement properties of a basic set of eight entangled three particle pure states possessing certain permutation symmetries are studied. They fall into four sets of two entangled states, differing in their patterns of robustness to…
We find the nearest product states for arbitrary generalized W states of n qubits, and show that the nearest product state is essentially unique if the W state is highly entangled. It is specified by a unit vector in Euclidean n-dimensional…
We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. Experimentally quantifying entanglement is highly desired for applications of quantum simulation experiments to fundamental…
The wedge product of vectors has been shown to yield the generalised entanglement measure I-concurrence, wherein the separability of the multiparty qubit system arises from the parallelism of vectors in the underlying Hilbert space of the…
The geometric measure of entanglement, originated by Shimony and by Barnum and Linden, is determined for a family of tripartite mixed states consisting of aribitrary mixtures of GHZ, W, and inverted-W states. For this family of states,…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
We present a new approach to the analysis of entanglement in smooth bipartite continuous-variable states. One or both parties perform projective filterings via preliminary measurements to determine whether the system is located in some…
We make a geometric study of the phases acquired by a general pure bipartite two level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
Quantifying experimentally created entanglement could in principle be accomplished by measuring the entire density matrix and calculating an entanglement measure of choice thereafter. Due to the tensor-structure of the Hilbert space, this…
We demonstrate that any pure bipartite state of two qubits may be decomposed into a superposition of a maximally entangled state and an orthogonal factorizable one. Although there are many such decompositions, the weights of the two…
We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides novel insight into the properties of…
Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise,…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
We consider quantum graph states that can be mapped to directed weighted graphs, also known as directed networks. The geometric measure of entanglement of the states is calculated for the quantum graph states corresponding to arbitrary…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…