GHZ-Equivalent State Distribution in Quantum Networks: Reducing Decoherence and Quantum Resource Consumption

As quantum networks scale, distributing entangled states like GHZ states becomes increasingly difficult due to decoherence, limited quantum memory, and topological constraints. The authors address the challenge of efficiently generating and distributing multipartite entangled states across repeater-based quantum networks while minimizing the noise exposure that degrades quantum fidelity.

The study introduces a distribution scheme for GHZ-equivalent star graph states. The core of the approach involves a merging procedure where two star graph states are combined by inserting an auxiliary qubit, followed by Y-basis measurements and local corrections. To optimize this process, the authors model the network as a weighted graph and use the Minimum Steiner Tree (MST) problem to select the most efficient paths between terminal nodes. By minimizing the total physical transmission distance, the scheme reduces the time qubits spend in transit, thereby mitigating decoherence. The authors implemented this scheme using the NetSquid simulation tool to verify its correctness and performance.

The proposed scheme achieves linear, O(N) scaling in both qubit usage and the number of controlled gates required for distribution. This efficiency is a significant improvement over existing methods that often introduce redundant entanglement structures. Simulation results confirm that the framework is practical for executing quantum communication protocols, such as quantum key distribution and secret sharing, by providing a robust method to establish multipartite entanglement across remote nodes.

Efficient entanglement distribution is a foundational requirement for the quantum internet. By reducing the resource overhead and the time-dependent decoherence of transmitted qubits, this scheme provides a scalable building block for complex quantum communication protocols. The ability to distribute star graph states efficiently allows for more reliable multipartite quantum communication in realistic, noisy network environments.