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 extract $n$-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 extractable $n$-qubits GHZ states and EPR pairs involving nodes remote in the artificial topology, as well as the achievable size $n$ of 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.