We investigate the general characters of fully entangled fraction for quantum states. The fully entangled fraction of Isotropic states and Werner states are analytically computed.

We present a way in identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable and genuine entangled states are explicitly given. The approach can be generalized to multipartite high dimensional case. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of quantum state with positive partial transpositions and the other is able to detect genuine entanglement. The results give an effective way in experimental entanglement identification.

Abstract. We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely related irreducible correlation. We point out differences between quantum states and probability vectors which exist in hierarchical models, in the divergence from a hierarchical model and in local maximizers of this divergence. The differences are, respectively, missing factorization, discontinuity and reduction of uncertainty. We discuss global maximizers of the mutual information of separable qubit states.

We introduce and study the l 1 norm of coherence of assistance both theoretically and operationally. We first provide an upper bound for the l 1 norm of coherence of assistance and show a necessary and sufficient condition for the saturation of the upper bound. For two and three dimensional quantum states, the analytical expression of the l 1 norm of coherence of assistance is given.Operationally, the mixed quantum coherence can always be increased with the help of another party's local measurement and one way classical communication since the l 1 norm of coherence of assistance, as well as the relative entropy of coherence of assistance, is shown to be strictly larger than the original coherence. The relation between the l 1 norm of coherence of assistance and entanglement is revealed. Finally, a comparison between the l 1 norm of coherence of assistance and the relative entropy of coherence of assistance is made.