Title: On the role of symmetry and geometry in global quantum sensing Show Chinese title

Title: 对称性和几何学在全局量子传感中的作用

Abstract: Global quantum sensing enables parameter estimation across arbitrary ranges with a finite number of measurements. Among the various existing formulations, the Bayesian paradigm stands as a flexible approach for optimal protocol design under minimal assumptions. Within this paradigm, however, there are two fundamentally different ways to capture prior ignorance and uninformed estimation; namely, requiring invariance of the prior distribution under specific parameter transformations, or adhering to the geometry of a state space. In this paper we carefully examine the practical consequences of both the invariance-based and the geometry-based approaches, and show how to apply them in relevant examples of rate and coherence estimation in noisy settings. We find that, while the invariance-based approach often leads to simpler priors and estimators and is more broadly applicable in adaptive scenarios, the geometry-based one can lead to faster posterior convergence in a well-defined measurement setting. Crucially, by employing the notion of location-isomorphic parameters, we are able to unify the two formulations into a single practical and versatile framework for optimal global quantum sensing, detailing when and how each set of assumptions should be employed to tackle any given estimation task. We thus provide a blueprint for the design of novel high-precision quantum sensors. Show Chinese abstract

Abstract: 全局量子传感使在有限测量次数下跨任意范围的参数估计成为可能。 在各种现有公式中，贝叶斯范式作为一种在最小假设下的最优协议设计灵活方法。 然而，在这个范式中，有两种根本不同的方式来捕捉先验无知和无信息估计；即要求先验分布在特定参数变换下保持不变，或者遵循状态空间的几何结构。 在本文中，我们仔细检查了基于不变性和基于几何的方法的实际后果，并展示了如何在噪声环境中的速率和相干性估计相关示例中应用它们。 我们发现，虽然基于不变性的方法通常会导致更简单的先验和估计器，并且在自适应场景中适用性更广，但基于几何的方法可以在定义明确的测量设置中导致更快的后验收敛。 关键的是，通过采用位置同构参数的概念，我们能够将两种公式统一为一个实用且多功能的框架，用于最优全局量子传感，详细说明在何时以及如何使用每组假设来解决任何给定的估计任务。 因此，我们提供了设计新型高精度量子传感器的蓝图。