存在不完美贝尔态测量的量子网络层析成像中的可辨识性与估计精度
Identifiability and Estimation Precision in Quantum Network Tomography with Imperfect Bell-State Measurements
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中文总结 AI 辅助
该研究针对不完美贝尔态测量下的量子网络层析成像，设计探针确保可辨识性并推导相关矩阵与估计器，证实其能在网络规模增大时维持链路参数估计精度稳定，均方误差随样本量趋近克拉美罗界。
中文摘要 AI 辅助
我们研究存在不完美贝尔态测量（BSMs）时用于端到端链路误差表征的量子网络层析成像（QNT），其中链路参数与测量参数间的乘性耦合使得可辨识性问题非平凡。对于n节点星型网络，我们设计探针以确保唯一可辨识性，推导费舍尔信息矩阵（FIM）与最大似然估计器（MLE）的闭式表达式，并通过克拉美罗界（CRB）表征估计精度。结果表明，BSM缺陷会降低估计精度，而所提探针在网络规模增大时能维持单个链路参数的精度基本稳定。蒙特卡洛模拟进一步证实，随着样本量增加，均方误差（MSE）趋近于CRB。
英文摘要
We study Quantum Network Tomography (QNT) for end-to-end link-error characterization under imperfect Bell-state measurements (BSMs), where multiplicative coupling between link and measurement parameters makes identifiability non-trivial. For an n-node star network, we design probes that ensure unique identifiability and derive closed-form expressions for the Fisher Information Matrix (FIM) and Maximum Likelihood Estimators (MLEs), and characterize estimation precision through the Cramer-Rao Bound (CRB). The results show that BSM imperfections degrade estimation precision, while the proposed probes maintain nearly stable precision for individual link parameters as the network size increases. Monte Carlo simulations further confirm that the Mean Squared Error (MSE) approaches the CRB with increasing sample size.
