Great effort has been made in the investigation of contextual correlations between compatible observables due to their both fundamental and practical importance. The graph-theoretic approach to correlate events has been proved to be an effective method in the characterization of quantum contextuality, which implies that quantum violations of noncontextual inequalities derived in the noncontextual hidden-variable models should be achievable. Finding experimentally more friendly and theoretically more powerful noncontextual inequalities associated with specific graphs is of particular interest. Here we consider Platonic graphs to vindicate the quantum maximum predicted by graph theory and test the quantum violation against the mixedness of the state. Among these solids we refer particularly to the icosahedron to build the experiment, as it gives rise to the largest quantum-classical difference. The contextual correlations are demonstrated on quantum four-dimensional states encoded in the spatial modes of single photons generated from a defect in a bulk silicon carbide. Our results shed new light on the conflict between quantum and classical physics and may promote deep understanding of the connection between quantum theory, graph theory, and operator theory.

中文翻译：

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通过柏拉图图进行量子相关性的实验测试

由于兼容的可观测对象的基本和实际重要性，已经在研究可观测对象之间的上下文相关性方面进行了巨大的努力。关联事件的图论方法已被证明是表征量子语境的一种有效方法，这意味着在非语境隐藏变量模型中得出的非语境不等式的量子违背应该是可以实现的。寻找与特定图形相关的实验上更友好，理论上更强大的非上下文不等式尤其令人感兴趣。在这里，我们考虑柏拉图图来证明由图论预测的最大量子，并针对状态的混合性测试量子违背。在这些固体中，我们特别指的是二十面体以进行实验，因为它引起了最大的量子经典差异。在以块状碳化硅中的缺陷产生的单个光子的空间模式下编码的量子四维态上证明了上下文相关性。我们的研究结果为量子物理学与经典物理学之间的冲突提供了新的思路，并可能增进对量子理论，图论和算子理论之间联系的深刻理解。