If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting (ii) associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality.

中文翻译：

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Kochen-Specker 论证中的交换性、可测性和上下文性

如果非上下文性被定义为系统对测量的响应相对于其他同时测量的鲁棒性，那么 Kochen-Specker 论证不提供量子上下文性的代数证明。即，要使论证有效，(i) 每个算子必须与测量唯一关联，(ii) 通勤算子必须表示同时测量。然而，在文献中讨论的所有 Kochen-Specker 论点中，(i) 或 (ii) 都没有得到满足。满足 (i) 的参数至少包含一个相互交换算子的子集，这些算子不代表同时测量，因此无法在物理上证明功能组合原则的合理性。