Saturating the quantum Cramér-Rao bound using LOCC

超越局部量子计量的全局界限

Global Bounds beyond Local Quantum Metrology

针对参数仅在宽域内已知的全局估计问题，通过引入全局得分函数和加权方差，建立了全局Cramér-Rao和Barankin型界限的层次结构，并给出了可实现的全局精度界限。

利用衍射光学神经网络实现量子极限成像

Quantum-limited imaging using diffractive optical neural networks

该研究将成像转化为多参数量子估计，提出基于衍射光学神经网络与光子计数的测量架构，可达到Nagaoka-Hayashi Cramér-Rao界，实现量子极限下的精细图像重建，性能优于直接成像，为相关领域应用开辟可扩展途径。

泽秒级单光子陀螺仪

Zeptosecond-scale single-photon gyroscope

本研究提出一种基于自发参量下转换的全光纤电信波段单光子陀螺仪，实现泽秒级延迟测量精度，资源效率接近理论极限，为量子光学与相对论结合的实验研究提供新路径。

Deterministic super-resolved estimation towards angular displacements based upon a Sagnac interferometer and parity measurement

Super-resolved angular displacement estimation is of crucial significances for quantum information process and optical lithography. Here we report on and experimentally demonstrate a protocol for angular displacement estimation based on a coherent state containing orbital angular momentum. In the lossless scenario, with using parity measurement, this protocol can theoretically achieve 4$\ell$-fold super-resolution with quantum number $\ell$, and shot-noise-limited sensitivity saturating the quantum Cramér-Rao bound. Several realistic factors and their effects are considered, including nonideal…

超分辨集体量子测量

Superresolving collective quantum measurements

本文提出利用置换对称性的集体测量方法，通过弱 Schur 采样和细化测量同时超分辨估计非相干玻色子混合信号的纯度、相对强度与间隔，并饱和多参数 Cramér-Rao 界。

Optimal condition for measurement observable via error-propagation

Propagation of error is a widely used estimation tool in experiments, where the estimation precision of the parameter depends on the fluctuation of the physical observable. Thus which observable is chosen will greatly affect the estimation sensitivity. Here we study the optimal observable for the ultimate sensitivity bounded by the quantum Cramér-Rao theorem in parameter estimation. By invoking the Schrödinger-Robertson uncertainty relation, we derive the necessary and sufficient condition for the optimal observables saturating the ultimate sensitivity for single parameter estimate. By applyin…

A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry

Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not attainable, leading to trade-offs in the attainable precisions. Here we study the simultaneous estimation of two parameters related to optical interferometry: phase and loss, using a fixed number of photons. We derive a trade-off in the estimation of these two parameters which shows that, in contrast to single-parameter estimation, it is impossible to design a strat…

Analytical techniques in single and multi-parameter quantum estimation theory: a focused review

As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to extract information from an unknown parameter embedded in a physical system such as the estimation converges to the true value of the parameter. According to the Cramér-Rao inequality in mathematical statistics, the Fisher information in the case of single-parameter estimation procedures, and the Fisher information matrix in the case of multi-parameter estimation…

Estimation of gradients in quantum metrology

We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of $N$ particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Usually gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two independent groups of particles. This approach, however, is sensitive to fluctuations of the off-set field determining the level-splitting of the particles and results in collective dephasing. In this work we use the framework of quantum metrology to assess…

宇称算符：在量子计量学中的应用

The Parity Operator: applications in quantum metrology

该文综述宇称算符在量子计量学多场景的应用，介绍其在拉姆齐光谱分辨率、原子宇称QND测量的原创结果，论证其作为最优可观测量的特性及在高精度原子钟的应用潜力。

Towards superresolution surface metrology: Quantum estimation of angular and axial separations

We investigate the localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using quantum metrology techniques, we show that a simultaneous estimation of the two separations is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cramér-Rao bound. Such a precision is not degraded in the sub-wavelength regime, thus overcoming the traditional limitations of classical direct imaging derived from Rayleigh's criterion. Our results are qualitatively independent of the po…

分布式量子多参数估计与最优局域测量

Distributed quantum multiparameter estimation with optimal local measurements

本研究提出分布式MZI阵列传感器，通过局域测量实现量子多参数估计，纠缠协议以单个非经典态达到灵敏度$1/\ar{n}_T^2$，相比独立方案获得$d$倍增益，克服散粒噪声极限。

单参数量子计量中的最优局域测量

Optimal Local Measurements in Single-Parameter Quantum Metrology

本研究针对量子计量中集体测量受限的问题，提出两种判定纯态量子比特系统能否通过局域测量饱和量子克拉美罗界的充要方法，推广了已有结果，为测量资源受限下的量子计量最优实现提供了新思路。