发表机构
University of the Basque Country UPV/EHU; EHU Quantum Center, University of the Basque Country UPV/EHU; School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham; Instituto de Física Corpuscular (IFIC), CSIC-Universitat de València and Departament de Física Teòrica, UV; Basque Center for Applied Mathematics (BCAM)（巴斯克大学; 巴斯克大学量子中心; 诺丁汉大学数学科学与量子非平衡系统数学与理论物理中心; 粒子物理研究所（IFIC），瓦伦西亚大学-CSIC及理论物理系，UV; 巴斯克应用数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于非对称右除超算子的量子Barankin界，为高斯态提供解析表达式，能捕捉标准量子Cramér-Rao界无法观察到的少样本阈值效应。
AI 中文摘要
我们提出了一种量子Barankin界作为量子参数估计中量子Cramér-Rao界的替代方案。量子Barankin界为在任意选择的参数点上满足任意选择的偏差约束的估计器的均方误差提供了下界。特别是，可以施加整个参数空间上的无偏性，从而为全局无偏的量子参数估计提供精度极限。与最近推导的基于对称除超算子的量子Barankin界相比，我们的界基于非对称的右除超算子。这一表述使我们能够找到高斯态的Barankin矩阵的解析表达式，从而能够高效计算该界。我们通过将结果应用于各种示例来展示其有用性，这些示例展示了少样本区域中的阈值效应，而标准量子Cramér-Rao界方法无法观察到这种效应。
英文摘要
We propose a quantum version of the Barankin bound as an alternative to the quantum Cramér-Rao bound for quantum parameter estimation. The quantum Barankin bound provides a lower bound on the mean squared error of estimators satisfying arbitrarily chosen bias constraints at arbitrarily chosen parameter points. In particular, unbiasedness over the entire parameter space can be imposed, yielding precision limits for globally unbiased quantum parameter estimation. In contrast to the recently derived quantum Barankin bound, which is based on a symmetric division superoperator, our bound is based on a nonsymmetric right-division superoperator. This formulation enables us to find analytic expressions for the Barankin matrix for Gaussian states, which allows for an efficient calculation of the bound. We demonstrate the usefulness of our results by applying them to various examples that exhibit the threshold effect in the few-shot regime, which is invisible to the standard quantum Cramér-Rao bound approach.
