Unveiling the nonclassicality within quasi-distribution representations through deep learning

Abstract 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.