发表机构
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于矩的框架量化Margenau--Hill准概率分布的非经典性，引入对数负性并推导下界、上界及正性阈值，支持多副本估计。
AI 中文摘要
准概率分布通过其与经典概率论的偏离，为描述量子系统的非经典特征提供了一种有用的方式。在本工作中，我们研究了与Margenau--Hill准概率（MHQ）分布相关的非经典性的量化问题，利用其矩而不需要重建完整的分布。首先，我们引入对数MHQ负性作为非经典性的量化指标，然后推导出一系列基于低阶矩的严格下界。在所得到的层级中，四阶矩界是基于偶数矩的界中最强的。对于量子比特，我们进一步推导了精确MHQ负性的紧上界，并确定了相应的极值态。我们还基于四阶矩获得了任意量子比特可观测量对的最优正性阈值。最后，我们展示了相关矩允许精确的多副本表示，为利用干涉测量或经典阴影技术进行估计提供了途径。我们的结果建立了一个基于矩的框架，用于从有限的一组低阶可观测量中提取关于MHQ负性的定量信息。
英文摘要
Quasiprobability distributions offer a useful way of describing nonclassical features of quantum systems through their departure from classical probability theory. In this work, we investigate the quantification of nonclassicality associated with the Margenau--Hill quasiprobability (MHQ) distribution using its moments, without requiring reconstruction of the full distribution. First we introduce the logarithmic MHQ negativity as a quantifier of nonclassicality, and then derive a hierarchy of rigorous lower bounds in terms of low-order moments. Within the resulting hierarchy, the fourth-moment bound is the strongest among the bounds based on even moments. For qubits, we further derive a tight upper bound on the exact MHQ negativity and identify the corresponding extremal state. We also obtain an optimal positivity threshold based on the fourth moment for arbitrary pairs of qubit observables. Finally, we show that the relevant moments admit exact multicopy representations, providing a route to their estimation using interferometry or classical shadow techniques. Our results establish a moment-based framework for extracting quantitative information about MHQ negativity from a finite set of low-order observables.
Comments20 pages, 4 figures
