Figure 1

Simplified, schematic structure of 4-partite states: the grey circles depict quantum states that are separable with respect to three different bipartitions (the biseparation $ABC-D$ and biseparations into pairs of subsystems are not shown). States that belong to two of these sets are at most bipartite entangled, and states that belong to all three sets are separable. Any convex sum of bipartite entangled states (depicted by ${\tau }_2$) is considered at most bipartite entangled, even though the state might not be separable with respect to any bipartition. Similarly, any convex sum of tripartite entangled states (depicted by ${\tau }_3$) is considered at most tripartite entangled. Only states that can not be obtained as a convex sum of at most tripartite entangled states are 4-partite entangled.Reuse & Permissions

Figure 2

Schematic representation of two pure five-partite states: a bipartite entangled (top) and a tripartite entangled (bottom). The bipartite entangled state is separable with respect to the 2-bipartitions ${\mathcal{S}}_1{\mathcal{S}}_2-{\mathcal{S}}_3{\mathcal{S}}_4{\mathcal{S}}_5$ and ${\mathcal{S}}_1{\mathcal{S}}_2{\mathcal{S}}_5-{\mathcal{S}}_3{\mathcal{S}}_4$. Indeed, any pure bipartite entangled five-partite state is biseparable with respect to at least two 2-bipartitions. Pure tripartite entangled five-partite states on the other hand can be separable with respect to one 2-bipartition only.Reuse & Permissions