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Entanglement detection beyond the computable cross-norm or realignment criterion
Optimal entanglement witnesses based on local orthogonal observables 
Detection of the maximally connected state
The maximally connected state (MCS) which was first introduced by Briegel and Raussendorf [Phys. Rev.Lett. 86, 910 (2001)] has many interesting properties in quantum information theory. Many important states that we are focusing on currently are included in this special set of states. We give a general criterion for MCS. When the ranks of all of the two-qubit reduced density matrices are two, we give a convenient criterion.
Compatibility relations between the reduced and global density matrices
It is a hard and important problem to find the criterion of a set of positive-definite matrices which can be written as reduced density operators of a multipartite global quantum state. This problem is closely related to the study of many-body quantum entanglement, which is one of the focuses of current quantum-information theory. We give several results on the necessary compatibility relations between a set of reduced and global density matrices.
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