AI 中文总结
该研究发展了核量子态估计（KQSE）方法，推导其收敛速率，实验表明该方法在非高斯连续变量量子态估计中具统计一致性与计算优势。
AI 中文摘要
我们进一步发展了核量子态估计（Kernel Quantum State Estimation, KQSE），这是一种完全由数据驱动的非参数方法，用于连续变量量子态的重构与表征，该方法源自我们近期的工作，以非参数核密度估计（Kernel Density Estimation, KDE）为基础。与依赖有限维基截断、参数化近似或先验模型的方法不同，KQSE 将对层析正交分布的特征函数的新型核估计器与合适的核积分变换相结合。特征函数直接从实验的零差或外差数据中估计，随后被变换以估计量子态的表示与特性，包括维格纳函数和密度矩阵核。我们注意到若干其他与物理相关的表示和特性可采用密切相关形式的变换，因此推导了基于 KQSE 的对应广泛类估计器的收敛速率。所得框架涵盖所有相空间表示、光子数层析图、量子态的迹乘积以及纯度。我们推导了这些核变换估计器的均方误差收敛速率，表明对应的 KQSE 应用继承了近最优速率 O(T^{-1})，其中 T 为测量总次数。所提出的理论同等适用于高斯和非高斯连续变量量子态，无需施加福克空间截断。针对模拟的高斯和非高斯态以及真实零差数据的数值实验，证明了 KQSE 相较于现有最优方法的优势，确立其为连续变量量子态估计与表征（尤其在非高斯领域）的统计一致且计算量适中的框架。
英文摘要
We further develop Kernel Quantum State Estimation (KQSE), a fully data-driven nonparametric method for continuous variable quantum state reconstruction and characterization, introduced in our recent work and rooted in nonparametric kernel density estimation (KDE). Unlike approaches relying on finite-dimensional basis truncations, parametric ansätze, or prior models, KQSE combines a new kernel estimator of the characteristic function of the tomographic quadrature distribution with suitable kernel integral transformations. The characteristic function is estimated directly from experimental homodyne or heterodyne data and subsequently transformed to estimate quantum state representations and characteristics, including the Wigner function and the density matrix kernel. Observing that several other physically relevant representations and characteristics admit transformations of a closely related form, we derive convergence rates for the corresponding broad class of KQSE-based estimators. The resulting framework covers all phase-space representations, the photon-number tomogram, trace products of quantum states, and purity. We derive mean squared error convergence rates for these kernel transformed estimators and show that the corresponding KQSE applications inherit the near optimal rate O(T^{-1}), where $T$ is the total number of measurements. The proposed theory applies equally to Gaussian and non-Gaussian continuous variable quantum states without imposing a Fock space cutoff. Numerical experiments on simulated Gaussian and non-Gaussian states and real homodyne data demonstrate the advantages of KQSE over state-of-the-art methods, establishing it as a statistically consistent and computationally modest framework for continuous variable quantum state estimation and characterization, particularly in the non-Gaussian regime.
Comments27 pages, 8 figures
