Separability properties of tripartite states with U circle times U circle times U symmetry - art. no. 042111

We study separability properties in a five-dimensional set of states of qua ntum systems composed of three subsystems of equal but arbitrary finite Hil bert space dimension. These are the states that can be written as linear co mbinations of permutation operators, or equivalently, commute with unitarie s of the form U x U x U. We compute explicitly the following subsets and th eir extreme points: (1) triseparable states, which are convex combinations of triple tensor products, (2) biseparable states, which are separable for a twofold partition of the system, and (3) states with positive partial tra nspose with respect to such a partition. Tripartite entanglement is investi gated in terms of the relative entropy of tripartite entanglement and of th e trace norm.