An ontological model is termed as maximally ψ-epistemic if the overlap between any two quantum states is fully accounted for by the overlap of their respective probability distributions of ontic states. However, in the literature, there exist two different mathematical definitions (termed here as 1MψE and 2MψE) that capture the equivalent notion of maximal ψ-epistemicity. In this work, we provide three theorems to critically examine the connections between preparation non-contextuality and the aforementioned two definitions of maximal ψ-epistemicity. In theorem 1, we provide a simple and direct argument of an existing proof to demonstrate that the mixed state preparation non-contextuality implies the first definition of maximal ψ-epistemicity. In theorem 2, we prove that the second definition of maximal ψ-epistemicity implies pure-state preparation non-contextuality. If both the definitions capture the equivalent notion of maximal ψ-epistemicity, then from the aforementioned two theorems one infers that the mixed-state preparation non-contextuality implies pure-state preparation non-contextuality. But, in theorem 3, we demonstrate that the mixed-state preparation non-contextuality in an ontological model implies pure-state contextuality and vice versa. This leads one to conclude that 1MψE and 2MψE capture inequivalent notions of maximal ψ-epistemicity. The implications of our results and their connections to other no-go theorems are discussed.

如果任何两个量子状态之间的重叠完全由它们各自的本体状态概率分布的重叠来解释，那么本体模型被称为最大ψ -epistemic。然而，在文献中，存在两种不同的数学定义（这里称为 1M ψ E 和 2M ψ E），它们捕获了最大ψ认识性的等效概念。在这项工作中，我们提供了三个定理来批判性地检查准备非上下文性与上述两个最大ψ定义之间的联系-认识论。在定理 1 中，我们提供了一个现有证明的简单而直接的论证，以证明混合状态准备非上下文性意味着最大ψ认识性的第一个定义。在定理 2 中，我们证明了最大ψ -epistemicity的第二个定义意味着纯状态准备非上下文性。如果这两个定义都捕获了最大ψ -认识性的等效概念，那么从上述两个定理可以推断出混合状态准备非上下文意味着纯状态准备非上下文。但是，在定理 3 中，我们证明了本体模型中的混合状态准备非上下文意味着纯状态上下文，反之亦然。这导致人们得出结论，1Mψ E 和 2M ψ E 捕获了最大ψ -认识性的不等价概念。讨论了我们的结果的含义及其与其他不成功定理的联系。