Entanglement manipulation of multipartite pure states with finite rounds of classical communication - David Sauerwein

We consider generic pure n-qubit states and a general class of pure states of arbitrary dimensions and arbitrarily many subsystems. We characterize those states which can be reached from some other state via local operations assisted by finitely many rounds of classical communication (LOCC_N). For n qubits with n>3, we show that this set of states is of measure zero. That is, almost no state can be reached if restricted to the practical scenario of LOCC_N. We also identify classes where any separable transformation can be realized by a protocol in which each step is deterministic (all-det-LOCC_N). Such transformations can be considered as natural generalizations of bipartite transformations. We show, however, that in general there exist state transformations which require a probabilistic step within the protocol. This highlights the difference between bipartite and multipartite LOCC and shows that multipartite LOCC transformations are more complex than the transformations considered in the literature so far. We also analyze an interesting genuinely multipartite effect that we call locking or unlocking the power of other parties. This means that one party can prevent or enable the implementation of LOCC transformations by other parties. Finally, we show how easily computable lower bounds on some entanglement measures can be obtained by restricting to LOCC_N.
This work was published in C. Spee, J. I. de Vicente, D. Sauerwein, and B. Kraus, Phys. Rev. Lett. 118, 040503 (2017) J. I. de Vicente, C. Spee, D. Sauerwein, and B. Kraus Phys. Rev. A 95, 012323 (2017)