In spite of its fundamental importance in quantum science and technology, the experimental certification of nonclassicality is still a challenging task, especially in realistic scenarios where losses and noise imbue the system. Here, we present the first experimental implementation of the recently introduced phase-space inequalities for nonclassicality certification, which conceptually unite phase-space representations with correlation conditions. We demonstrate the practicality and sensitivity of this approach by studying nonclassicality of a family of noisy and lossy quantum states of light. To this end, we experimentally generate single-photon-added thermal states with various thermal mean photon numbers and detect them at different loss levels. Based on the reconstructed Wigner and Husimi $Q$ functions, the inequality conditions detect nonclassicality despite the fact that the involved distributions are nonnegative, which includes cases of high losses (93%) and cases where other established methods do not reveal nonclassicality. We show the advantages of the implemented approach and discuss possible extensions that assure a wide applicability for quantum science and technologies.

中文翻译：

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通过相空间不等式进行非经典性的实验证明

尽管其在量子科学和技术中的根本重要性，但非经典性的实验认证仍然是一项艰巨的任务，尤其是在损耗和噪声会影响系统的现实情况下。在这里，我们介绍了最近引入的用于非经典性证明的相空间不等式的第一个实验实现，它在概念上将相空间表示与相关条件结合在一起。我们通过研究光的嘈杂和有损量子状态族的非经典性，证明了这种方法的实用性和敏感性。为此，我们通过实验生成具有各种热平均光子数的添加了单光子的热态，并在不同的损耗水平下对其进行检测。基于重建的Wigner和Husimi$问$尽管所涉及的分布是非负的，但不平等条件仍然可以检测到函数的非经典性，其中包括高损失（93％）的情况以及其他已建立方法未显示出非经典性的情况。我们展示了已实现方法的优势，并讨论了可能的扩展，这些扩展确保了量子科学和技术的广泛适用性。