Fidelity estimation is a crucial component for the quality control of entanglement distribution networks. This work studies a scenario in which multiple nodes share noisy Greenberger-Horne-Zeilinger (GHZ) states. Due to the collapsing nature of quantum measurements, the nodes randomly sample a subset of noisy GHZ states for measurement and then estimate the average fidelity of the unsampled states conditioned on the measurement outcome. By developing a fidelity-preserving diagonalization operation, analyzing the Bloch representation of GHZ states, and maximizing the Fisher information, the proposed estimation protocol achieves the minimum mean squared estimation error in a challenging scenario characterized by arbitrary noise and the absence of prior information. Additionally, this protocol is implementation-friendly as it only uses local Pauli operators according to a predefined sequence. Numerical studies demonstrate that, compared to existing fidelity estimation protocols, the proposed protocol reduces estimation errors in both scenarios involving independent and identically distributed (i.i.d.) noise and correlated noise.

翻译：保真度估计是纠缠分发网络质量控制的关键环节。本研究探讨多节点共享含噪Greenberger-Horne-Zeilinger（GHZ）态的场景。由于量子测量的坍缩特性，节点随机选取部分含噪GHZ态进行测量，并依据测量结果估计未采样态的平均保真度。通过构建保真度保持对角化操作、分析GHZ态的Bloch表示、以及最大化Fisher信息，所提出的估计协议在任意噪声且无先验信息的挑战性场景中实现了最小均方估计误差。此外，该协议仅需按预定序列使用局域Pauli算符，具有友好的可实现性。数值研究表明，相较于现有保真度估计方案，本协议在独立同分布噪声与关联噪声场景下均能降低估计误差。