General pure multipartite entangled states and the Segre variety

We introduce an intuitive measure of genuine multipartite entanglement which is based on the well-known concurrence. We show how lower bounds on this measure can be derived that also meet important characteristics of an entanglement measure. These lower bounds are experimentally implementable in a feasible way enabling quantification of multipartite entanglement in a broad variety of cases.

Concurrence, introduced by Hill and Wootters [Phys. Rev. Lett. 78, 5022 (1997)], provides an important measure of entanglement for a general pair of qubits that is faithful: strictly positive for entangled states and vanishing for all separable states. Such a measure captures the entire content of entanglement, providing necessary and sufficient conditions for separability. We present an extension of concurrence to multiparticle pure states in arbitrary dimensions by a new fr...

Entanglement monotones, such as the concurrence, are useful tools to characterize quantum correlations in various physical systems. The computation of the concurrence involves, however, difficult optimizations and only for the simplest case of two qubits a closed formula was found by Wootters [Phys. Rev. Lett. 80, 2245 (1998)]. We show how this approach can be generalized, resulting in lower bounds on the concurrence for higher dimensional systems as well as for multipartite ...

We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entanglement.

This paper presents a new measure of entanglement which can be employed for multipartite entangled systems. The classification of multipartite entangled systems based on this measure is considered. Two approaches to applying this measure to mixed quantum states are discussed.

In this paper, a new measure of entanglement for general pure bipartite states of two qutrits is formulated.

We present proper genuine multipartite entanglement (GME) measures for arbitrary multipartite and dimensional systems. By using the volume of concurrence regular polygonal pyramid we first derive the GME measure of four-partite quantum systems. From our measure it is verified that the GHZ state is more entangled than the W state. Then we study the GME measure for multipartite quantum states in arbitrary dimensions. A well defined GME measure is constructed based on the volume...

We study the entanglement of multipartite quantum states. Some lower bounds of the multipartite concurrence are reviewed. We further present more effective lower bounds for detecting and qualifying entanglement, by establishing functional relations between the concurrence and the generalized partial transpositions of the multipartite systems.

We construct nonlinear multiparty entanglement measures for distinguishable particles, bosons and fermions. In each case properties of an entanglement measures are related to the decomposition of the suitably chosen representation of the relevant symmetry group onto irreducible components. In the case of distinguishable particles considered entanglement measure reduces to the well-known many particle concurrence. We prove that our entanglement criterion is sufficient and nece...

In this paper, we introduce a category of one-parameter bipartite entanglement quantifiers, termed $G_q$-concurrence ($q>1$), and show rigorously that they satisfy all the axiomatic conditions of an entanglement measure and can be considered as a generalization of concurrence. In addition, we establish an analytic formula relating $G_q$-concurrence to concurrence for $1<q\leq2$ in two-qubit systems. Furthermore, the polygamy relation is presented based on the $G_q$-concurrenc...