Quantum contextuality, a more general quantum correlation, is an important resource for quantum computing and quantum information processing. Meanwhile, quantum contextuality plays an important role in fundamental quantum physics. Yu and Oh (YO) proposed a proof of the Kochen–Specker theorem for a qutrit with only 13 rays. Here, we further study quantum contextuality of YO-13 rays using the inequality approach. The maximum quantum violation value of the optimal noncontextuality inequality constructed by YO-13 rays is increased to 11.9776 in the four-dimensional system, which is larger than 11.6667 in the qutrit system. The result shows that the set of YO-13 rays has stronger quantum contextuality in the four-dimensional system. Moreover, we provide an all-versus-nothing proof (i.e. Hardy-like proof) to study YO-13 rays without using any inequality, which is easily applied to experimental tests. Our results will further deepen the understanding of YO-13 rays.

中文翻译：

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YO-13 射线的量子背景

量子上下文是一种更普遍的量子相关性，是量子计算和量子信息处理的重要资源。同时，量子上下文在基础量子物理学中起着重要作用。Yu 和 Oh (YO) 提出了 Kochen-Specker 定理的证明，即只有 13 条射线的 qutrit。在这里，我们使用不等式方法进一步研究 YO-13 射线的量子上下文。YO-13射线构造的最优非上下文不等式的最大量子违反值在四维系统中增加到11.9776，大于qutrit系统中的11.6667。结果表明，YO-13射线的集合在四维系统中具有更强的量子关联性。此外，我们提供了一个全无证明（即 Hardy-like 证明）来研究 YO-13 射线，而不使用任何不等式，这很容易应用于实验测试。我们的研究结果将进一步加深对 YO-13 射线的理解。