AI 中文总结
本研究提出融入物理约束的压缩感知框架，在数据匮乏场景下通过凸优化提升量子传感的参数估计性能，可降低误差且无需额外硬件资源。
AI 中文摘要
量子传感器有望达到海森堡极限的测量灵敏度，但实际中其性能常受噪声、有限采样和实现缺陷的影响。本研究提出一种通用框架，通过利用时域关联函数的内在结构约束来改进此类场景下的参数估计。该方法基于 Kemper 等人[PRL 132, 160403 (2024)]的发现：厄米可观测量的双时间关联函数生成的 Gram 矩阵为半正定矩阵，而实验获取的数据可能违反该性质。我们将信号重构建模为凸优化问题，强制满足半正定性、托普利茨（Toeplitz）结构和由基础动力学驱动的低秩先验。我们通过分析证明，在合适条件下，无噪声场景中可唯一识别真实信号，有噪声场景中可稳定恢复信号。我们还基于 GHZ 基磁力计协议进行数值验证，结果显示，强制这些物理约束可显著提升稀疏含噪数据的频率估计性能，尤其在数据匮乏 regime（仅少量时间采样）下，该方法相比矩阵 pencil 技术等标准谱估计方法，能提供更优且稳定的改进。尽管重构信号通常未达到散粒噪声极限性能，但所提方法可持续降低估计误差并恢复信号的大量基础结构。这些结果表明，将通用物理约束融入数据分析，无需额外硬件资源或校准即可提升量子传感协议的实际性能。
英文摘要
Quantum sensors promise measurement sensitivities that can scale at the Heisenberg limit, but in practice their performance is often degraded by noise, finite sampling, and implementation imperfections. In this work we present a general framework for improving parameter estimation in such settings by exploiting intrinsic structural constraints of time-domain correlation functions. Our approach builds on the observation of Kemper et al. [PRL 132, 160403 (2024)] that two-time correlation functions of Hermitian observables generate Gram matrices that are positive semidefinite, a property that can be violated in experimentally acquired data. We formulate signal reconstruction as a convex optimization problem that enforces positive semidefiniteness, Toeplitz structure, and low-rank priors motivated by the underlying dynamics. We show analytically that, under suitable conditions, the ground-truth signal can be uniquely identified in the noiseless case and recovered stably in the presence of noise. We further demonstrate numerically, in a GHZ-based magnetometry protocol, that enforcing these physical constraints can significantly improve frequency estimation from sparse and noisy data. In particular, we observe a clear advantage in the data-starved regime, where only a small number of time samples are available and standard spectral estimation methods, including matrix pencil techniques, provide limited or unstable improvement over direct fitting. While the reconstructed signals do not in general reach the shot-noise-limited performance, the proposed approach consistently reduces estimation error and recovers much of the underlying structure of the signal. These results indicate that incorporating universal physical constraints into data analysis can enhance the practical performance of quantum sensing protocols without requiring additional hardware resources or calibration.
Comments10 pages, 6 figures
Journal refQuantum Sci. Technol. 11 035072 (2026)
