论文标题
用于操作微调的数学框架
A mathematical framework for operational fine tunings
论文作者
论文摘要
在本体论模型的框架中，量子理论的固有非分类特征似乎总是涉及经过微调的属性，即在操作层面上具有但在本体论层面中断的属性。它们在操作层面上的外观是由于本体论参数无法解释的特殊选择，这是我们的微调所指。这种特征的著名示例是上下文性和非局部性。在本文中，我们开发了一个独立于理论的数学框架来表征操作微调。这些与因果微调不同 - 伍德和斯宾肯斯已经在[NJP，17 033002（2015）]中引入 - 因为操作微调的定义不涉及有关基本因果结构的任何假设。我们展示了如何进行操作微调的示例，例如Spekkens广泛的上下文性，违反贝尔实验中的参数独立性以及本体论时间不对称性，适合我们的框架。我们讨论了寻找新的微调的可能性，并使用该框架为非局部性和广义上下文之间的关系提供了新的启示。尽管非局部性通常被认为是一种情境性的一种形式，但只有当非局部性由违反参数独立性组成时，这才是正确的。我们还使用函子的概念在类别理论的语言中制定框架。
In the framework of ontological models, the inherently nonclassical features of quantum theory always seem to involve properties that are fine tuned, i.e. properties that hold at the operational level but break at the ontological level. Their appearance at the operational level is due to unexplained special choices of the ontological parameters, which is what we mean by a fine tuning. Famous examples of such features are contextuality and nonlocality. In this article, we develop a theory-independent mathematical framework for characterizing operational fine tunings. These are distinct from causal fine tunings -- already introduced by Wood and Spekkens in [NJP,17 033002(2015)] -- as the definition of an operational fine tuning does not involve any assumptions about the underlying causal structure. We show how known examples of operational fine tunings, such as Spekkens' generalized contextuality, violation of parameter independence in Bell experiment, and ontological time asymmetry, fit into our framework. We discuss the possibility of finding new fine tunings and we use the framework to shed new light on the relation between nonlocality and generalized contextuality. Although nonlocality has often been argued to be a form of contextuality, this is only true when nonlocality consists of a violation of parameter independence. We formulate our framework also in the language of category theory using the concept of functors.
