Quantum theory shows a striking nonclassical feature of contextuality, which is also a crucial resource for quantum information processing. In this paper, we study the dependence of violating noncontextuality inequalities against the dimension of quantum systems. To this end, we consider the restrictions imposed on relations among measurements by limitation of dimensions. Based on the graph-theoretic approach to quantum contextuality, we construct noncontextuality inequalities using multiple mutually orthogonal projectors which are unique to high-dimensional quantum systems. We report two typical classes of dimension-dependent noncontextuality inequalities for one of which a violation implies the dimension of the quantum system is higher than a threshold, and for the other, different amounts of violations correspond to different thresholds of dimension. Our paper is expected to inspire more dimension-dependent noncontextuality inequalities.

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具有大上下文的维度相关的非上下文不等式

量子理论显示了上下文的显着非经典特征，这也是量子信息处理的重要资源。在本文中，我们研究了违反非上下文不等式对量子系统维度的依赖性。为此，我们考虑通过维度限制对测量之间的关系施加的限制。基于量子上下文的图论方法，我们使用多个相互正交的投影仪构建非上下文不等式，这些投影仪是高维量子系统独有的。我们报告了两种典型的维度相关的非上下文不等式，其中一种违规意味着量子系统的维度高于阈值，而对于另一种，不同数量的违规对应不同的维度阈值。我们的论文有望激发更多与维度相关的非上下文不等式。