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We consider generic pure $n$-qubit states and a general class of pure statesof arbitrary dimensions and arbitrarily many subsystems. We characterize thosestates which can be reached from some other state via Local Operations assistedby finitely many rounds of Classical Communication ($LOCC_{\mathbb{N}}$). For$n$ qubits with $n>3$ we show that this set of states is of measure zero, whichimplies that the maximally entangled set is generically of full measure ifrestricted to the practical scenario of $LOCC_{\mathbb{N}}$. Moreover, weidentify a class of states for which any $LOCC_{\mathbb{N}}$ protocol can berealized via a concatenation of deterministic steps. We show, however, that ingeneral there exist state transformations which require a probabilistic stepwithin the protocol, which highlights the difference between bipartite andmultipartite LOCC.

Entangled pure state transformations via local operations assisted by finitely many rounds of classical communication