Keiji matsumoto
Two important classes of the quantum statistical model, the locally quasi-classical model and the quasi-classical model, are introduced from the estimation theoretical viewpoint, and they are characterized geometrically by the vanishing conditions of the relative phase factor (RPF), implying the close tie between Uhlmann parallel transport and the quantum estimation theory.
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Quantifying Uhlmann curvature from Yang-Mills action and its implications in quantum multiparameter estimation
本文提出一个量化乌尔曼曲率的标量，探讨其在量子多参数估计中的测量不兼容性，证明其规范不变性和重参数不变性，并以相位和相位扩散联合估计为例计算曲率。
Quantum algorithms for Uhlmann transformation
本文提出了在查询和样本访问模型中实现Uhlmann变换的量子算法，对低秩态实现了多项式时间的指数级改进，并推导了复杂度下界，大幅提升了保真度估计等任务的效率。
This post is the author's doctoral dissertation back in 1997. The dissertation covers following four kinds of problems: First, it studies achievable Cramer-Rao type bounds of various multi-parameter pure state models. Second, it relates CR-bouds, both of mixed state and pure states, with Berry-Uhlmann curvature. Roughly, it characterize how the statistical model differs from classical probability distribution family. Though the relation is rather qualitative for mixed states, the quantitative relation is obtained for pure state models. Third topic is relation between Berry-Uhlmann geometry and…
Optimal fidelity estimation when one state is pure via algorithmic Uhlmann transform
本研究移除了纯态Uhlmann保真度估计需预知哪个态为纯态的先验要求，通过特化改进型算法Uhlmann变换，在仅知两态有一纯态的条件下实现了最优保真度估计。
Joint estimation of noise and nonlinearity in Kerr systems
本文针对含自Kerr相互作用的有损与退相位信道，利用QFIM及零差、双零差测量分析损耗/退相位与非线性的联合估计极限，揭示增强、退化及不可同时最优的条件。
Gradients, parallelism, and variance of quantum estimates
本文提出了一种基于LCU电路的通用梯度框架，用于计算量子估计的梯度，并分析了其收敛行为及在近期和容错硬件中的应用。
Joint quantum estimation of loss and nonlinearity in driven-dissipative Kerr resonators
本文针对相干驱动耗散Kerr谐振器，联合估计损耗率与非线性耦合，证明模型渐近经典且QFI随时间和驱动增强，正交探测可反复逼近QFI。
Efficient fidelity estimation: Alternative derivation and related applications
本文通过函数幂级数展开和迹函数性质，为量子态保真度的简化表达式提供了替代证明，并拓展了新型不相似函数和复杂迹函数的研究。
In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér-Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium…
Multi-parameter quantum metrology with discrete-time quantum walks
针对离散时间量子行走，本文推导一般硬币算符的 QFIM，证明三参数中仅两个可估计且模型渐近经典，并用于 Dirac 模型电荷与质量同时估计。
Enhancement in temperature sensing of a reservoir by Kerr-nonlinear resonator
提出利用带驱动的Kerr非线性谐振腔精确测量量子储层温度的估计技术，通过量子Fisher信息评估证明增加Kerr非线性系数和驱动幅度可显著提升估计精度，并发现最优零差检测优于外差检测。
Dimension matters: precision and incompatibility in multi-parameter quantum estimation models
该研究探究多参数量子估计中探针维度对精度界与不相容性的影响，证明了维度与参数数量的关系对估计可行性及不相容程度的作用，同时指出渐近不相容性测度的局限性与独特价值。
We investigate two special classes of two-mode Gaussian states of light that are important from both the experimental and theoretical points of view: the mode-mixed thermal states and the squeezed thermal ones. Aiming to a parallel study, we write the Uhlmann fidelity between pairs of states belonging to each class in terms of their defining parameters. The quantum Fisher information matrices on the corresponding four-dimensional manifolds are diagonal and allow insightful parameter estimation. The scalar curvatures of the Bures metric on both Riemannian manifolds of special two-mode Gaussian …
Low Cost Bayesian Experimental Design for Quantum Frequency Estimation with Decoherence
针对量子频率估计问题，提出低成本自适应贝叶斯实验设计策略WES，通过经验性成本降低技术实现低优化开销与高度并行性，数值模拟表明其性能最可靠且达到Heisenberg极限。
Towards Deploying Optimistic Quantum Fourier Transforms: An Architecture-Algorithm Co-Design Study
本文研究了在可重构中性原子硬件上基于表面码容错执行模型的乐观量子傅里叶变换架构-算法协同设计，提出热区架构以动态路由资源包，分析不同热区数量对并行性和延迟的影响，并识别算法-架构瓶颈。
Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in general. In this work, we introduce hybrid quantum-classical algorithms for these two distance measures on near-term quantum devices where no assumption of input state is required. First, we introduce the Variational Trace Distance Estimation (VTDE) algorithm. We in particular provide the technique to extract the desired spectrum information of any Hermitian …
Fidelity Estimation to a Known Quantum State Is Nearly Quadratic in the Smaller Rank
该研究解决了未知态与已知秩-$r$参考态的根乌尔曼保真度估计的样本复杂度问题，确定其为$\boldsymbol{\tilde{\theta}}(r^2/\boldsymbol{\theta}^2)$，还得到量子谱估计的近二次下界并明确了该区域样本复杂度的多项式阶。
A Unified Complexity Framework for Quantum Property Testing
该研究提出了一个量子泛函估计的统一下界框架，推导了多种量子属性测试问题的近紧下界，证明了20多种量子算法的最优性。
Polynomial-time certification of fidelity for many-body mixed states and mixed-state universality classes
本文提出一种多项式时间算法，用于高效计算许多体混合态的保真度下界和上界，通过变分优化量子电路并提取临界指数，提升量子系统验证的精度。
Multiparameter quantum bounds for entanglement-assisted aperture synthesis
本研究将纠缠辅助孔径合成建模为多参数估计，证明QFI可约化，纠缠恢复部分信息，并给出最优接收机与纠缠分配方案，为量子成像提供设计目标。
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