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.

Three-tangle for the rank-three mixture composed of Greenberger-Horne-Zeilinger, W and flipped W states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere S 8 of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle.The physical implication of three-tangle is briefly discussed.

Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n − 1)-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure n-qudit states have reduced states of (n-1)-qudits, which are equivalent under local unitary(LU) transformations, then they have equal Groverian and Geometric entanglement measures. Second, both measures have an upper bound for pure states. However, this upper bound is reached only for two qubit systems. Third, it converts effectively the nonlinear eigenvalue problem for three qubit Groverian measure into linear eigenvalue equations. Some typical solutions of these linear equations are written explicitly and the features of the general solution are discussed in detail.