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

Title: 在对称性和几何学在全局量子传感中的作用

Abstract: Global sensing enables parameter estimation across arbitrary parameter ranges with a finite number of shots. While various formulations exist, the Bayesian paradigm offers a flexible approach to optimal protocol design under minimal assumptions. However, there are several sets of assumptions capturing the notions of prior ignorance and uninformed estimation, leading to two main approaches: invariance of the prior distribution under specific parameter transformations, and adherence to the geometry of a state space. While the first approach often leads to simpler priors and estimators and is more broadly applicable in adaptive settings, the second can lead to faster posterior convergence in a well-defined measurement setting. We examine the practical consequences of both approaches and show how to apply them in examples of rate and coherence estimation in noisy scenarios. More importantly, by employing the notion of location-isomorphic parameters, we unify the two approaches into a practical and versatile framework for optimal global quantum sensing, detailing when and how each set of assumptions should be employed - a blueprint for the design of quantum sensors. Show Chinese abstract

Abstract: 全局感知能够在任意参数范围内，使用有限次数的测量进行参数估计。 虽然存在各种公式，但贝叶斯范式在最少假设下提供了一种灵活的最优协议设计方法。 然而，有一些假设集捕捉了先验无知和无信息估计的概念，导致两种主要方法：先验分布在特定参数变换下的不变性，以及遵循状态空间的几何结构。 虽然第一种方法通常会导致更简单的先验和估计器，并且在自适应设置中应用更广泛，但第二种方法在定义明确的测量设置中可以更快地实现后验收敛。 我们研究了这两种方法的实际后果，并展示了如何在噪声场景中的速率和相干性估计示例中应用它们。 更重要的是，通过采用位置同构参数的概念，我们将这两种方法统一为一个实用且通用的框架，用于最优全局量子感知，详细说明何时以及如何使用每组假设——这是量子传感器设计的蓝图。