We investigate a model of the interacting holographic dark energy with cold dark matter (CDM). If the holographic energy density decays into CDM, we find two types of the effective equation of state. In this case we have to use the effective equations of state ($\omega^{\rm eff}_{\rm \Lambda}$) instead of the equation of state ($\omega_{\rm \Lambda})$. For a fixed ratio of two energy densities, their effective equations of state are given by the same negative constant. Actually, the cosmic anti-friction arisen from the vacuum decay process may induce the acceleration with $\omega^{\rm eff}_{\rm \Lambda}<-1/3$. For a variable ratio, their effective equations of state are slightly different, but they approach the same negative constant in the far future. Consequently, we show that such an interacting holographic energy model cannot accommodate a transition from the dark energy with $\omega^{\rm eff}_{\rm \Lambda}\ge-1$ to the phantom regime with $\omega^{\rm eff}_{\rm \Lambda}<-1$.Comment: 11 pages, 2 eps figures, final version to appear in PL

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.

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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.

The finite temperature effect is examined in Randall-Sundrum brane-world scenario with inclusion of the matter fields on the brane. At zero temperature it is found that the theory on the brane is conformally invariant, which guarantees AdS/CFT. At 4d effective action we derived a temperature-dependent nonvanishing cosmological constant at the flat spacetime limit of brane worldvolume. At the cosmological temperature 3K the cosmological constant is roughly (0.0004eV ) 4 which is within the upper bound of the recent experimental value (0.01eV ) 4 *