On the Efficient Extraction of Entangled Resources

In the Quantum Internet, multipartite entanglement enables a rich and dynamic overlay topology, referred to as artificial topology, upon the physical one, that can be exploited for communication purposes. In fact, the ability to extractn-qubits GHZ states and EPR pairs from the original multipartite entangled state constitutes the resource primitives for end-to-end and on-demand quantum communications. Thus, in this paper, we theoretically determine upper and lower bounds for the number of extractablen-qubits GHZ states and EPR pairs involving nodes remote in the artificial topology, as well as the achievable sizenof remote GHZ states. The theoretical analysis is then complemented by the proposal of a novel algorithm, which provides in polynomial-time a heuristic solution to the above problem. This is remarkable, since the theoretical problem is NP-complete. The performance analysis demonstrates the proposed algorithm is able to effectively manipulate the original and arbitrary graph state for extracting entanglement resources across remote nodes.