Bound entanglement and distillability of multipartite quantum systems

TL;DR

This paper constructs and classifies multipartite quantum states in three-qubit systems, revealing bound entanglement and distillability properties, and extends these results to larger systems with higher dimensions.

Contribution

It introduces a class of entangled states with specific distillability properties and generalizes findings from three-qubit to higher-dimensional systems.

Findings

States are bound entangled for (AB)-C split

States are NPT and 1-copy undistillable for A-(BC) and B-(AC) splits

Results generalized to 2n x 2n x 2n 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.