One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this work, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.
Hierarchy of saturation conditions for multiparameter quantum metrology bounds
Institute of Systems and Information Engineering, University of Tsukuba（筑波大学系统信息工程学院）；Center for Artificial Intelligence Research (C-AIR), University of Tsukuba（筑波大学人工智能研究中心）；Institute of Fundamental and Transdisciplinary Research, Institute of Quantum Sensing, and Institute for Advanced Study in Physics, Zhejiang University（浙江大学基础与跨学科研究院、量子传感研究所、物理高等研究院）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院和斯德哥尔摩大学）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所（CNR-INO））；European Laboratory for Nonlinear Spectroscopy (LENS)（欧洲非线性光谱学实验室）
Gaussian Quantum Metrology with Realistic Linear Sensors
Laboratoire Astroparticule et Cosmologie, Université Paris Cité, CNRS（粒子与宇宙学实验室，巴黎西岱大学，法国国家科学研究中心）；Pritzker School of Molecular Engineering, University of Chicago（普里茨克分子工程学院，芝加哥大学）；Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理研究所，耶路撒冷希伯来大学）；Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics, California Institute of Technology（理论天体物理学，沃尔特·伯克理论物理研究所，加州理工学院）
Strict hierarchy between $n$-wise measurement simulability, compatibility structures, and multi-copy compatibility
Inria, CPHT, LIX, CNRS, École polytechnique, Institut Polytechnique de Paris（法国国家信息与自动化研究所、高等计算与理论物理中心、信息处理实验室、法国国家科学研究中心、巴黎综合理工学院、巴黎理工学院）；Department of Physics “E. Fermi”, University of Pisa（比萨大学“恩里科·费米”物理学系）；Sorbonne Université, CNRS, LIP6（索邦大学、法国国家科学研究中心、信息处理实验室）
Quantum time-flip beats adaptive metrology: Asymptotic benefit, activation, and unsimulability
Indian Institute of Science Education and Research（印度科学教育与研究所）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Networked Quantum Devices Unit, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学量子设备网络单元）；Université Paris-Saclay（巴黎萨克雷大学）
Optimal Strategies for Multi-parameter Quantum Metrology
The Chinese University of Hong Kong（香港中文大学）；The University of Hong Kong（香港大学）；The Hong Kong Institute of Quantum Information Science and Technology（香港量子信息科学与技术研究所）
Quantum hypothesis testing of non-mixed-unitarity: A multifaceted hierarchy of quantum channel discrimination
Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；IT:U Interdisciplinary Transformation University（IT:U 跨学科转型大学）
Quantization of Physical Interaction Strengths via Singular Moduli
State Key Laboratory for Precision Spectroscopy, ECNU, Shanghai（精密光谱学国家重点实验室，华东师范大学）；Dept. of Chemistry/Physics, University of California, Irvine（加州大学尔湾分校化学/物理系）；QuMorpheus Invitiative（QuMorpheus倡议）
