发表机构
School of Electrical Engineering, Korea University; Quantum Network Research Center, Korea Institute of Science and Technology Information（韩国大学电气工程学院; 韩国科学技术信息研究院量子网络研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于EAQEC码扩展结构的纠缠辅助稳定子框架，实现分布式局域相位传感、返回误差识别及传感后逻辑态保留，稳定子读出达到量子费舍尔信息，估计器趋近$1/\beta$标度。
AI 中文摘要
分布式量子传感需要空间分离的探针获取局域参数，同时保持与网络级量子信息处理的兼容性。我们开发了一种基于纠缠辅助量子纠错（EAQEC）码扩展结构的纠缠辅助稳定子框架，其中预共享纠缠比特（ebit）的远端半部分直接用作局域相位探针，而联合态同时携带编码的逻辑子系统。每个远端探针获取局域Z轴相位，随后通过X型噪声通道返回。在扩展的EAQEC稳定子结构中，包含$X_{B_j}$的稳定子提供相位依赖的测量统计，而其包含$Z_{B_j}$的伙伴则记录对应的返回误差校正子。我们引入图编码公式以明确该结构，同时给出示例[[5,1,3;2]]构造。我们进一步表明，在联合传感-校正子测量记录的条件下，传感后态与原始编码态仅相差一个已知的泡利变换，因此逻辑信息仍可用于后续编码操作。对于此处考虑的局域相位模型，稳定子读出达到可用的量子费舍尔信息，而有限次测量的估计器随重复次数增加趋近于相应的$1/\beta$标度。因此，该框架为分布式局域相位传感、受限返回误差识别及传感后逻辑态保留提供了通用的纠缠辅助稳定子结构，不依赖于EAQEC本身固有的计量增强。
英文摘要
Distributed quantum sensing requires spatially separated probes to acquire local parameters while maintaining compatibility with network-level quantum information processing. We develop an entanglement-assisted stabilizer framework based on the extended structure of entanglement-assisted quantum error-correcting (EAQEC) codes, in which the remote halves of pre-shared ebits are used directly as local phase probes while the joint state simultaneously carries an encoded logical subsystem. Each remote probe acquires a local Z-axis phase and subsequently returns through an X-type noise channel. Within the extended EAQEC stabilizer structure, the stabilizer containing $X_{B_j}$ provides phase-dependent measurement statistics, whereas its partner containing $Z_{B_j}$ records the corresponding return-error syndrome. A graph-code formulation is introduced to make this structure explicit, together with an illustrative [[5,1,3;2]] construction. We further show that, conditioned on the joint sensing-and-syndrome measurement record, the post-sensing state differs from the original encoded state only by a known Pauli transformation, so that the logical information remains available for subsequent encoded operations. For the local-phase model considered here, the stabilizer readout attains the available quantum Fisher information, while the finite-shot estimator approaches the corresponding $1/\sqrt{M}$ scaling as the number of repetitions increases. The framework therefore provides a common entanglement-assisted stabilizer structure for distributed local-phase sensing, restricted return-error identification, and post-sensing logical-state retention, without relying on an intrinsic metrological enhancement from EAQEC itself.
