Related papers: Evaluating the geometric measure of multiparticle …
The concept of relative state is used to introduce geometric phases that originate from correlations in states of composite quantum systems. In particular, we identify an entanglement-induced geometric phase in terms of a weighted average…
Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
We define a multi-partite entanglement measure for stabilizer states, which can be computed efficiently from a set of generators of the stabilizer group. Our measure applies to qubits, qudits and continuous variables.
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated…
Quantifying genuine entanglement is a crucial task in quantum information theory. Based on the geometric mean of bipartite $\alpha$-concurrences among all bipartitions, we present a class of well-defined genuine multipartite entanglement…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation…
The main concern of this paper is how to define proper measures of multipartite entanglement for mixed quantum states. Since the structure of partial separability and multipartite entanglement is getting complicated if the number of…
We consider the mixed three-qubit bound entangled state defined as the normalized projector on the subspace that is complementary to an Unextendible Product Basis [C. H. Bennett et. al., Phys. Rev. Lett. 82, 5385 (1999)]. Using the fact…
We discuss entanglement of multiparticle quantum systems. We propose a potential measure of a type of entanglement of pure states of n qubits, the n-tangle. For a system of two qubits the n-tangle is equal to the square of the concurrence,…
Recently, Meyer and Wallach [D.A. Meyer and N.R. Wallach (2002), J. of Math. Phys., 43, pp. 4273] proposed a measure of multi-qubit entanglement that is a function on pure states. We find that this function can be interpreted as a physical…
To determine whether a given multipartite quantum state is separable with respect to some partition we construct a family of entanglement measures R_m. This is done utilizing generalized concurrences as building blocks which are defined by…
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and…
The quantification and classification of quantum entanglement is a very important and still open question of quantum information theory. In this paper, we describe an entanglement measure for multipartite pure states (the minimum of…
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum states.…
We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $d$-dimensional bipartite and multipartite systems. The criterion for bipartite quantum…
We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express…
In this paper, we study the multipartite entanglement properties of graph states up to seven qubits. Our analysis shows that the generalized concurrence measure is more efficient than geometric entanglement measure for measuring…
A general description of entanglement is suggested as an action realized by an arbitrary operator over given disentangled states. The related entanglement measure is defined. Because of its generality, this definition can be employed for…