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arXiv · 2508.18024

Polynomial-time Extraction of Entanglement Resources

Si-Yi Chen·Angela Sara Cacciapuoti·Marcello Caleffi
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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.

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Si-Yi Chen, Angela Sara Cacciapuoti, Marcello Caleffi. 2025-08-25. Polynomial-time Extraction of Entanglement Resources. https://doi.org/10.1109/qce65121.2025.00130

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