Lower Bounds of Concurrence for Multipartite States

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.Comment: 13 page

Global Entanglement for Multipartite Quantum States

Based on the residual entanglement [9] (Phys. Rev. A \textbf{71}, 044301 (2005)), we present the global entanglement for a multipartite quantum state. The measure is shown to be also obtained by the bipartite partitions of the multipartite state. The distinct characteristic of the global entanglement is that it consists of the sum of different entanglement contributions. The measure can provide sufficient and necessary condition of fully separability for pure states and be conveniently extended to mixed states by minimizing the convex hull. To test the sufficiency of the measure for mixed states, we evaluate the global entanglement of bound entangled states. The properties of the measure discussed finally show the global entanglement is an entanglement monotone.Comment: 6 page

Measures and dynamics of entangled states

We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for different, realistic experimental scenarios.Comment: Physics Reports, in pres

Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation

Quantum entanglement plays crucial roles in quantum information processing. Quantum entangled states have become the key ingredient in the rapidly expanding field of quantum information science. Although the nonclassical nature of entanglement has been recognized for many years, considerable efforts have been taken to understand and characterize its properties recently. In this review, we introduce some recent results in the theory of quantum entanglement. In particular separability criteria based on the Bloch representation, covariance matrix, normal form and entanglement witness; lower bounds, subadditivity property of concurrence and tangle; fully entangled fraction related to the optimal fidelity of quantum teleportation and entanglement distillation will be discussed in detail.Comment: 63 pages, 4 figure

Evaluable multipartite entanglement measures: are multipartite concurrences entanglement monotones?

We discuss the monotonicity under local operations and classical communication (LOCC) of systematically constructed quantities aiming at quantification of entanglement properties of multipartite quantum systems. The so-called generalized multipartite concurrences can qualify as legitimate entanglement measures if they are monotonous under LOCC. In the paper we give a necessary and sufficient criterion for their monotonicity.Comment: 7 pages, 1 figure, minor changes - clarity of proofs improve

Operational Classification and Quantification of Multipartite Entangled States

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.Comment: 14 pages, RevTex4, published versio

Multi-partite analysis of average-subsystem entropies

So-called average subsystem entropies are defined by first taking partial traces over some pure state to define density matrices, then calculating the subsystem entropies, and finally averaging over the pure states to define the average subsystem entropies. These quantities are standard tools in quantum information theory, most typically applied in bipartite systems. We shall first present some extensions to the usual bipartite analysis, (including a calculation of the average tangle, and a bound on the average concurrence), follow this with some useful results for tripartite systems, and finally extend the discussion to arbitrary multi-partite systems. A particularly nice feature of tri-partite and multi-partite analyses is that this framework allows one to introduce an "environment" for small subsystems to couple to.Comment: Minor changes. 1 reference added. Published versio

Lower Bound of Multipartite Concurrence Based on Sub-quantum State Decomposition

We study the entanglement of tripartite quantum states and provide analytical lower bound of concurrence in terms of the concurrence of sub-states. The lower bound may improve all the existing lower bounds of concurrence. The approach is generalized to arbitrary dimensional multipartite systems.Comment: 5 page