Separable Multipartite Mixed States: Operational Asymptotically Necessary and Sufficient Conditions

We introduce an operational procedure to determine, with arbitrary probability and accuracy, optimal entanglement witnesses for every multipartite entangled state. This method provides an operational criterion for separability which is asymptotically necessary and sufficient. Our results are also generalized to detect all different types of multipartite entanglement.

Figure 1

$\mathrm{T}\mathrm{r}(\mathbf{(}{W}_{\mathrm{o}\mathrm{p}\mathrm{t}}\rho (a)\mathbf{)}\times a$, for the $3\times 3$ Horodecki bound entangled states.

Figure 2

Percentage of wrong results in X number of samples ($N$), for $2\times 2$ (dashed line) and $2\times 3$ (solid line) systems.