Bound entanglement and distillability of multipartite quantum systems

We construct a class of entangled states in $\mathcal{H}={\mathcal{H}}_A\otimes {\mathcal{H}}_B\otimes {\mathcal{H}}_C$ quantum systems with $dim{\mathcal{H}}_A=dim{\mathcal{H}}_B=dim{\mathcal{H}}_C=2$ and classify those states with respect to their distillability properties. The states are bound entanglement for the bipartite split$(AB)-C$. The states are NPT entanglement and $1$-copy undistillable for the bipartite splits $A-(BC)$ and $B-(AC)$. Moreover, we generalize the results of $2\otimes 2\otimes 2$ systems to the case of $2n\otimes 2n\otimes 2n$ systems.