量子科学与技术的重大突破要求更高效地分析量子多体态。该领域的一个重大挑战是验证实验室中量子设备制备的量子态是否准确匹配所需的目标纯态。随机测量技术的最新进展为该领域提供了新的见解。具体而言，经典阴影层析和阴影重叠等协议已被提出。在这些进展的基础上，我们研究了通过随机局域 Haar 测量认证纯量子态方案的基本性质。我们推导出适用于任意特定估计器构造的样本涨落界限。这些界限依赖于用于估计保真度的可观测量的算符尺寸分布，或任意可观测量的约化密度矩阵的有效变化。我们的结果揭示了算符复杂性与量子算法效率之间的内在相互作用，这构成了对具有长程纠缠的纯态进行局域认证的障碍。
英文摘要：
Remarkable breakthroughs in quantum science and technology are demanding for more efficient methods in analyzing quantum many-body states. A significant challenge in this field is to verify whether a quantum state prepared by quantum devices in the lab accurately matches the desired target pure state. Recent advancements in randomized measurement techniques have provided fresh insights in this area. Specifically, protocols such as classical shadow tomography and shadow overlap have been proposed. Building on these developments, we investigate the fundamental properties of schemes that certify pure quantum states through random local Haar measurements. We derive bounds for sample fluctuations that are applicable regardless of the specific estimator construction. These bounds depend on the operator size distribution of either the observable used to estimate fidelity or the valid variation of the reduced density matrix for arbitrary observables. Our results unveil the intrinsic interplay between operator complexity and the efficiency of quantum algorithms, serving as an obstacle to local certification of pure states with long-range entanglement.
Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements
虽然最近已经证明了如何以设备无关的方式证明任何纯两量子比特纠缠态的最大随机性[E。Woodhead等人，Phys. Rev. Research 2，042028（R）（2020）]，来自更高局部维度的纠缠态的最佳随机性认证的问题仍然是开放的。在这里，我们介绍了一种方法的设备无关的认证的最大可能数量的$2\log_23$随机比特使用纯二分纠缠两quutrit状态和极端的九个结果一般非投影测量。为此，我们利用最近在[S. Sarkar等人，arXiv：2110.15176]，它结合了一种设备无关的方法来证明三维希尔伯特空间中的完全Weyl-Heisenberg基，以及一种单侧设备无关的方法来证明两个quitri部分纠缠态。
Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario
Lund University（隆德大学）；University of Jyväskylä（于韦斯屈莱大学）；Technical University of Denmark（丹麦技术大学）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
Semi-Device-Independent Certification for Nonlocality without Entanglement
Faculty of Information Technology, University of Jyväskylä（于韦斯屈莱大学信息技术学院）；School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院电气工程学院）
Bounding many-body properties under partial information and finite measurement statistics
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学与技术研究院）；Qilimanjaro Quantum Tech.（基利曼贾罗量子技术公司）；ICREA - Institució Catalana de Recerca i Estudis Avançats（ICREA-加泰罗尼亚高级研究学院）；Physics Department E. Pancini, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学E. Pancini物理系）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli（意大利国家核物理研究所（INFN）那不勒斯分部）
Resource efficient certification of system environment entanglement solely from reduced system dynamics
National Cheng Kung University（国立成功大学）；Center for Quantum Frontiers of Research & Technology, NCKU（量子前沿研究与技术中心，国立成功大学）；RIKEN Center for Quantum Computing, RIKEN（理研量子计算中心，理研）；Institute of Spintronics and Quantum Information, Faculty of Physics and Astronomy, Adam Mickiewicz University（亚当·密茨凯维奇大学物理与天文学学院自旋电子学与量子信息研究所）；Physics Department, The University of Michigan（密歇根大学物理系）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
Certification of high-dimensional entanglement in continuous-variable systems
Technische Universität Wien, Atominstitut & Vienna Center for Quantum Science and Technology (VCQ)（维也纳工业大学，原子研究所与维也纳量子科学与技术中心）；Charles University, Faculty of Mathematics and Physics（查理大学，数学与物理学院）
Certifying classes of $d$-outcome measurements with quantum steering
Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）；Institute of Fundamental Technological Research, Polish Academy of Sciences（波兰科学院基础技术研究所以）
The Power of Two Bases: Robust and copy-optimal certification of nearly all quantum states with few-qubit measurements
Paul G. Allen School of Computer Science and Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学系）；Massachusetts Institute of Technology（麻省理工学院）
Near-optimal quantum metrology with few-qubit measurements
Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；Oratomic（奥拉托米克公司）；Perimeter Institute for Theoretical Physics（理论物理珀蒂默研究所）；University of Waterloo（滑铁卢大学）
Bounding Kirkwood-Dirac negativity of Gaussian processes
University of Florence（佛罗伦萨大学）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所（CNR-INO））；Università di Bologna and INFN, Sezione di Bologna（博洛尼亚大学和意大利国家核物理研究所博洛尼分所）；Paderborn University（帕德博恩大学）
Certifying bipartite entangled states with few local measurements: from separable stabilizers to applications
Universitat Autònoma de Barcelona（巴塞罗那自治大学）；ICREA—Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究与高等研究所）；Universität zu Köln（科隆大学）；Technische Universität München（慕尼黑工业大学）
Certifying fermionic Gaussian states (and a little more) with optimal precision dependence
The Institute for Fundamental Study (IF), Naresuan University（纳瑞苏安大学基础研究所）；Chula Intelligent and Complex Systems Center of Excellence, Department of Physics, Faculty of Science, Chulalongkorn University（朱拉隆功大学理学院物理系查拉智能与复杂系统卓越中心）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）
