To unequivocally distinguish genuine quantumness from classicality, a widely adopted approach focuses on the negative values of a quasi-distribution representation as compelling evidence of nonclassicality. Prominent examples include the dynamical process nonclassicality characterized by the canonical Hamiltonian ensemble representation (CHER) and the nonclassicality of quantum states characterized by the Wigner function. However, to construct a multivariate joint quasi-distribution function with negative values from experimental data is typically highly cumbersome. Here we propose a computational approach utilizing a deep generative model, processing three marginals, to construct the bivariate joint quasi-distribution functions. We first apply our model to tackle the challenging problem of the CHERs, which lacks universal solutions, rendering the problem ground-truth (GT) deficient. To overcome the GT deficiency of the CHER problem, we design optimal synthetic datasets to train our model. While trained with synthetic data, the physics-informed optimization enables our model to capture the detrimental effect of the thermal fluctuations on nonclassicality, which cannot be obtained from any analytical solutions. This underscores the reliability of our approach. This approach also allows us to predict the Wigner functions subject to thermal noises. Our model predicts the Wigner functions with a prominent accuracy by processing three marginals of probability distributions. Our approach also provides a significant reduction of the experimental efforts of constructing the Wigner functions of quantum states, giving rise to an efficient alternative way to realize the quantum state tomography.

中文翻译：

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通过深度学习揭示准分布表示中的非经典性


为了明确区分真正的量子性和经典性，一种广泛采用的方法侧重于准分布表示的负值，作为非经典性的令人信服的证据。突出的例子包括以规范哈密顿集成表示 （CHER） 为特征的动力学过程非经典性，以及以 Wigner 函数为特征的量子态的非经典性。然而，从实验数据中构造一个具有负值的多元联合准分布函数通常非常麻烦。在这里，我们提出了一种利用深度生成模型的计算方法，处理三个边际，以构建二元联合准分布函数。我们首先应用我们的模型来解决具有挑战性的 CHER 问题，该问题缺乏通用解决方案，导致问题真实 （GT） 不足。为了克服 CHER 问题的 GT 缺陷，我们设计了最佳合成数据集来训练我们的模型。在使用合成数据进行训练时，基于物理学的优化使我们的模型能够捕捉到热波动对非经典性的不利影响，这是任何解析解都无法获得的。这凸显了我们方法的可靠性。这种方法还允许我们预测受热噪声影响的 Wigner 函数。我们的模型通过处理概率分布的三个边际来预测 Wigner 函数，具有突出的准确性。我们的方法还显着减少了构建量子态的 Wigner 函数的实验工作，从而产生了一种实现量子态断层扫描的有效替代方法。