Tripartite entanglement is examined when one of the three parties moves with a uniform acceleration with respect to other parties. As the Unruh effect indicates, tripartite entanglement exhibits a decreasing behavior with increasing acceleration. Unlike bipartite entanglement, however, tripartite entanglement does not completely vanish in the infinite acceleration limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger or W state initially, the corresponding π -tangle, one of the measures of tripartite entanglement, is shown to be π/6 ∼ 0.524 or 0.176 in this limit, respectively. This fact indicates that tripartite quantum-information processing may be possible even if one of the parties approaches the Rindler horizon. The physical implications of this striking result are discussed in the context of black-hole physics.

Which state does lose less quantum information between GHZ and W states when they are prepared for two-party quantum teleportation through noisy channel? We address this issue by solving analytically a master equation in the Lindbald form with introducing the noisy channels which makes the quantum channels to be mixed states. It is found that the answer of the question is dependent on the type of the noisy channel. If, for example, the noisy channel is (L 2,x , L 3,x , L 4,x )-type where L ′ s denote the Lindbald operators, GHZ state is always more robust than W state, i.e. GHZ state preserves more quantum information. In, however, (L 2,y , L 3,y , L 4,y )-type channel the situation becomes completely reversed. In (L 2,z , L 3,z , L 4,z )-type channel W state is more robust than GHZ state when the noisy parameter (κ) is comparatively small while GHZ state becomes more robust when κ is large. In isotropic noisy channel we found that both states preserve equal amount of quantum information. A relation between the average fidelity and entanglement for the mixed state quantum channels are discussed.

It is known that relative entropy of entanglement for an entangled state ρ is defined via its closest separable (or positive partial transpose) state σ. Recently, it has been shown how to find ρ provided that σ is given in two-qubit system. In this paper we study on the reverse process-i.e., how to find σ provided that ρ is given. It is shown that if ρ is one of Bell-diagonal, generalized Vedral-Plenio, and generalized Horodecki states, one can find σ from a geometrical point of view. This is possible due to the following two facts: (i) The Bloch vectors of ρ and σ are identical with each other (ii) The correlation vector of σ can be computed from a crossing point between a minimal geometrical object, in which all separable states reside in the presence of Bloch vectors, and a straight line, which connects the point corresponding to the correlation vector of ρ and the nearest vertex of the maximal tetrahedron, where all two-qubit states reside. It is shown, however, that these nice properties are not maintained for the arbitrary two-qubit states.

A method is developed to derive algebraic equations for the geometric measure of entanglement of threequbit pure states. The equations are derived explicitly and solved in the cases of most interest. These equations allow one to derive analytic expressions of the geometric entanglement measure in a wide range of three-qubit systems, including the general class of W states and states which are symmetric under the permutation of two qubits. The nearest separable states are not necessarily unique, and highly entangled states are surrounded by a one-parametric set of equally distant separable states. A possibility for physical applications of the various three-qubit states to quantum teleportation and superdense coding is suggested from the aspect of entanglement.

Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound. However, for multipartite states the standard Schmidt decomposition generally does not exist. We use a generalized Schmidt decomposition and the geometric measure of entanglement to characterize three-qubit pure states and derive a single-parameter family of maximally entangled three-qubit states. The paradigmatic Greenberger-Horne-Zeilinger (GHZ) and W states emerge as extreme members in this family of maximally entangled states. This family of states possess different trends of entanglement behavior: in going from GHZ to W states the geometric measure, the relative entropy of entanglement, and the bipartite entanglement all increase monotonically whereas the three-tangle and bi-partition negativity both decrease monotonically.