paper

Polynomial-time Extraction of Entanglement Resources

arXiv:2508.18024 · doi:10.1109/QCE65121.2025.00130

Abstract

The extraction of EPR pairs and n-qubits GHZ states among remote nodes in quantum networks constitutes the resource primitives for end-to-end and on-demand communications. However, the Bell-VM problem, which determines whether a given graph state can be transformed into a set of Bell pairs on specific vertices (not necessarily remote), is known to be NP-complete. In this paper, we extend this problem, not only by focusing on nodes remote within generic graph states, but also by determining the number of extractable n-qubit remote GHZ states -- beside the number of remote EPR pairs. The rationale for tackling the extraction of GHZ states among remote nodes, rather than solely remote EPR pairs, is that a GHZ state enables the dynamic extraction of an EPR pair between any pair of nodes sharing the state. This, in turn, implies the ability of accommodating the traffic requests on-the-fly. Specially, we propose a polynomial-time algorithm for solving the aforementioned NP-complete problem. Our results demonstrate that the proposed algorithm is able to effectively adapt to generic graph states for extracting entanglement resources across remote nodes.

arXiv commentAccepted manuscript for publication in Proc. of IEEE International Conference on Quantum Computing and Engineering (QCE), 2025. This work has been funded by the European Union under Horizon Europe ERC-CoG grant QNattyNet ("Quantum-Native Communication Networks: from Quantum Message to Quantum Functioning"), n.101169850. Details at https://qnattynet.quantuminternet.it

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