Abstract:
We consider the method of entanglement witness operator to verify genuine multipartite entanglement for single-particle W states involving N parties. In particular, linear optical schemes using photo detectors and beam splitters are proposed to implement two different types of witness operator in experiment. The first scheme that requires only a single measurement setting is shown to detect genuine multipartite entanglement for the overall efficiency beyond 1-1/N. On the other hand, the second scheme with N+1 measurement settings achieves success at a significantly lowered efficiency than 1-1/N.

Abstract:
We propose two classes of the generalized concurrence vectors of the multipartite systems consisting of qubits. Making use of them, we are able to, respectively, describe and quantify GHZ-class and W-class entanglement both in total and between arbitrary two partite in the multipartite system consisting of qubits. In the case of pure state of three qubits that one partite is separable, it is shown to exactly back to the usual Wootters' concurrence after introduce a whole concurrence vector. In principle, our method is applicable to any $N$-partite systems consisting of $N$ qubits.

Abstract:
We study the dynamics of multipartite entanglement under the influence of decoherence. A suitable generalization of concurrence reveals distinct scaling of the entanglement decay rate of GHZ and W states, for various environments.

Abstract:
We propose a unified mathematical scheme, based on a classical tensor isomorphism, for characterizing entanglement that works for pure states of multipartite systems of any number of particles. The degree of entanglement is indicated by a set of absolute values of the determinants for each subspace of the multipartite systems. Unlike other schemes, our scheme provides indication of the degrees of entanglement when the qubits are measured or lost successively, and leads naturally to the necessary and sufficient conditions for multipartite pure states to be separable. For systems with a large number of particles, a rougher indication of the degree of entanglement is provided by the set of mean values of the determinantal values for each subspace of the multipartite systems.

Abstract:
A scheme to generate three qubit maximally entangled W-states, using three trapped ions interacting with red sideband tuned single mode field of a high finesse cavity, is proposed. For the cavity field initially prepared in a number state, the probability of generating three ion W-state is calculated. By using the ion-cavity coupling strengths achieved in experimental realizations, the interaction time needed for W-state generation is found to be of the order of 10 $\mu $ sec. It is found that for a fixed number of photons in the cavity the nature of entanglement of ionic internal states can be manipulated by appropriate choice of initial state phonon number. The ionic qubits in W-like state are found to be entangled to cavity photons. Analytical expressions for global negativity and partial $K-$way negativities (K=2 to 4) are obtained to study the evolution of entanglement distribution as a function of interaction parameter. Reversible entanglement exchange between different entanglement modes is observed. For specific values of interaction parameter, the three ions and photon-phonon system are found to have four partite entanglement, generated by 2-way and 3-way correlations.

Abstract:
We study the occurrence of multipartite entanglement in spin chains. We show that certain genuine multipartite entangled states, namely W states, can be obtained as ground states of simple XX type ferromagnetic spin chains in a transverse magnetic field, for any number of sites. Moreover, multipartite entanglement is proven to exist even at finite temperatures. A transition from a product state to a multipartite entangled state occurs when decreasing the magnetic field to a critical value. Adiabatic passage through this point can thus lead to the generation of multipartite entanglement.

Abstract:
Nonlinearity and entanglement are two important properties by which physical systems can be identified as non-classical. We study the dynamics of the resonant interaction of up to N=3 two-level systems and a single mode of the electromagnetic field sharing a single excitation dynamically. We observe coherent vacuum Rabi oscillations and their nonlinear speed up by tracking the populations of all qubits and the resonator in time. We use quantum state tomography to show explicitly that the dynamics generates maximally entangled states of the W class in a time limited only by the collective interaction rate. We use an entanglement witness and the threetangle to characterize the state whose fidelity F=78% is limited in our experiments by crosstalk arising during the simultaneous qubit manipulations which is absent in a sequential approach with F=91%.

Abstract:
We investigate the presence of multipartite entanglement in macroscopic spin chains. We discuss the Heisenberg and the XY model and derive bounds on the internal energy for systems without multipartite entanglement. Based on this we show that in thermal equilibrium the above mentioned spin systems contain genuine multipartite entanglement, even at finite modest temperatures.

Abstract:
First, we show how the quantum circuits for generating and measuring multi-party entanglement of qubits can be translated to continuous quantum variables. We derive sufficient inseparability criteria for $N$-party continuous-variable states and discuss their applicability. Then, we consider a family of multipartite entangled states (multi-party multi-mode states with one mode per party) described by continuous quantum variables and analyze their properties. These states can be efficiently generated using squeezed light and linear optics.

Abstract:
The scheme for entanglement teleportation is proposed to incorporate multipartite entanglement of four qubits as a quantum channel. Based on the invariance of entanglement teleportation under arbitrary two-qubit unitary transformation, we derive relations of separabilities for joint measurements at a sending station and for unitary operations at a receiving station. From the relations of separabilities it is found that an inseparable quantum channel always leads to a total teleportation of entanglement with an inseparable joint measurement and/or a nonlocal unitary operation.