AI 中文总结
该研究聚焦连接经典与量子物理概率形式体系中纠缠态经典概率生成问题，提出双协方差模型，利用高斯过程性质将其约简到二阶统计量，简化并推广了构造，阐明了并发度的经典概率意义。
AI 中文摘要
我们提出了一种新方法来解决连接经典与量子物理概率形式体系的问题，聚焦于其最具挑战性的方面：纠缠态的经典概率生成。我们表明复合量子系统密度算符中编码的统计量对应于四阶经典统计量。具体而言，生成密度算符时必须考虑随机协方差算符的协方差，我们将此框架称为双协方差模型（DCM）。这种双协方差具有由两个不同时间尺度相互作用产生的非平凡内部结构，结合了时间和统计协方差。本文利用高斯过程的一个著名性质：二阶矩决定高阶矩，特别是四阶矩。这种高斯约简通过将DCM约简到二阶统计量来简化它。利用（循环）高斯过程简化并推广了纠缠态的DCM构造，使其在数学上更严谨，还阐明了纠缠的基本定量度量——并发度的经典概率意义。
英文摘要
We propose a novel approach to the problem of interconnecting the probabilistic formalisms of classical and quantum physics, focusing on its most challenging aspect: the classical probabilistic generation of entangled states. We show that the statistics encoded in the density operators of composite quantum systems correspond to fourth-order classical statistics. Specifically, to generate a density operator, one must consider the covariance of a random covariance operator. We term this framework the Double Covariance Model (DCM). This double covariance possesses a non-trivial internal structure that arises from the interplay between two distinct time scales, combining temporal and statistical covariances. In this article, we exploit a well-known property of Gaussian processes: the second-order moment determines the moments of higher orders, specifically the fourth-order moment. This Gaussian reduction simplifies the DCM by reducing it to second-order statistics. Utilizing (circular) Gaussian processes simplifies and generalizes the DCM construction for entangled states, rendering it mathematically rigorous. Furthermore, it clarifies the classical probabilistic meaning of concurrence, a foundational quantitative measure of entanglement.
CommentsInvited talk at QIP26 conference, Vaxjoe, June 2026
