I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: (i) each operator is uniquely realized by a single physical measurement; (ii) commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating (i), another violating (ii), and a third one violating both (i) and (ii).

中文翻译：

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Peres-Mermin平方的三个非上下文隐藏变量模型

我将争辩说，如果没有为操作符提供满足以下两个要求的物理解释，则Peres-Mermin平方并不一定排除值确定（确定性）非上下文隐藏变量模型：（i）每个操作符都由一个唯一地实现单一物理测量；（ii）通勤操作员通过同时测量来实现。为了支持这一主张，我将为Peres-Mermin广场的三种不同物理实现构造三个隐藏变量模型：一个违反（i），另一个违反（ii），第三个违反（i）和（ii）。