  Entanglement theory is formulated as a quantum resource theory in which the
free operations are local operations and classical communication (LOCC). This
defines a partial order among bipartite pure states that makes it possible to
identify a maximally entangled state, which turns out to be the most relevant
state in applications. However, the situation changes drastically in the
multipartite regime. Not only do there exist inequivalent forms of entanglement
forbidding the existence of a unique maximally entangled state, but recent
results have shown that LOCC induces a trivial ordering: almost all pure
entangled multipartite states are incomparable (i.e. LOCC transformations among
them are almost never possible). In order to cope with this problem we consider
alternative resource theories in which we relax the class of LOCC to operations
that do not create entanglement. We consider two possible theories depending on
whether resources correspond to multipartite entangled or genuinely
multipartite entangled (GME) states and we show that they are both non-trivial:
no inequivalent forms of entanglement exist in them and they induce a
meaningful partial order (i.e. every pure state is transformable to more weakly
entangled pure states). Moreover, we prove that the resource theory of GME that
we formulate here has a unique maximally entangled state, the generalized GHZ
state, which can be transformed to any other state by the allowed free
operations.
