论文标题
最大$ψ$的两个定义 - 上学本体论模型和制备非上下文性
Two definitions of maximally $ψ$-epistemic ontological model and preparation non-contextuality
论文作者
论文摘要
如果任何两个量子状态之间的重叠是由它们各自的ONTIC状态的概率分布的重叠完全解释的，则将本体学模型称为最大$ψ$ pepistlectip。但是，在文献中，存在两个不同的数学定义（此处称为1M $ψ$ e和2M $ψ$ e），它们捕获了最大$ψ$ - peSTOSISTOMIDITY的等效概念。在这项工作中，我们提供了三个定理，以批判性地检查制备非上下文性与上述最大$ψ$ - 认知性的两个定义之间的联系。在定理1中，我们提供了现有证据的简单而直接的论点，以证明混合状态制备非上下文性意味着最大$ψ$ - 普遍性的第一个定义。在定理2中，我们证明了最大$ψ$ - 普遍性的第二个定义意味着纯状态制备非上下文性。如果两个定义都捕获了最大$ψ$ - 普遍性的等效概念，则从上述两个定理中，一个渗透混合状态制备非上下文性的一个含义意味着纯状态的制剂非上下文性。但是，在定理-3中，我们证明了本体论模型中的混合状态制备非上下文性意味着纯状态的情境性，反之亦然。这导致人们得出结论，1M $ψ$ e和2M $ $ E E捕获的最大$ψ$ - pepistecity的概念。讨论了我们的结果的含义及其与其他无关定理的联系。
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 literature, there exists the two different mathematical definitions (termed here as 1M$ψ$E and 2M$ψ$E) 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 1M$ψ$E and 2M$ψ$E capture inequivalent notion of maximal $ψ$-epistemicity. The implications of our results and their connections to other no-go theorems are discussed.
