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Entanglement is the resource to overcome the restriction of operations toLocal Operations assisted by Classical Communication (LOCC). The MaximallyEntangled Set (MES) of states is the minimal set of n-partite pure states withthe property that any truly n-partite entangled pure state can be obtaineddeterministically via LOCC from some state in this set. Hence, this setcontains the most useful states for applications. In this work we characterizethe MES for generic three qutrit states. Moreover, we analyze which genericthree qutrit states are reachable (and convertible) under LOCC transformations.To this end we study reachability via separable operations (SEP), a class ofoperations that is strictly larger than LOCC. Interestingly, we identify afamily of pure states that can be obtained deterministically via SEP but notvia LOCC. To our knowledge these are the first examples of transformationsamong pure states that can be implemented via SEP but not via LOCC.

The MES of tripartite qutrit states and pure state separable transformations which are not possible via LOCC