Polynomial-time Extraction of Entanglement Resources

TL;DR

This paper presents a polynomial-time algorithm for extracting entanglement resources, including EPR pairs and GHZ states, from generic graph states in quantum networks, enabling dynamic and efficient quantum communication.

Contribution

It introduces a novel polynomial-time solution for a complex NP-complete problem related to entanglement extraction in quantum networks, extending previous work to include GHZ states.

Findings

Algorithm effectively extracts entanglement resources from generic graph states.

Enables dynamic, on-demand quantum communication by extracting GHZ states.

Demonstrates polynomial-time complexity for a previously NP-complete problem.

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.