Bound entanglement and distillability of multipartite quantum systems

Abstract

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 \(2\otimes2\otimes2\) systems to the case of \(2n\otimes 2n\otimes2n\) systems.