通过上下文依赖公理系统的类量子系统的经典表示
Classical representations for quantum-like systems through an axiomatics for context dependence
摘要：
我们引入了一个“隐藏测量系统”的定义，即，- 物理实体，对于该物理实体存在：（i）“所研究的实体的一组非上下文状态”和（ii）“测量上下文的一组状态”，并且使得所有不确定性都是由于缺乏对测量上下文的实际状态的了解。首先，我们确定一个明确的标准，使我们能够验证是否一个给定的隐藏的测量系统是一个给定的夫妇$\Si,{\cal E}$的一组状态$\Si$和一组测量${\cal E}$（$=$测量系统）组成的表示。然后，我们证明了每个测量系统，存在至少一个表示作为一个隐藏的测量系统与$[0,1]$作为一组状态的测量上下文。因此，我们可以应用这个隐藏测量系统的定义来强加上下文依赖的公理。我们表明，以这种方式，我们总是找到经典表示（隐藏的测量表示）一般的非经典实体（例如量子实体）。
英文摘要：
We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are such that all uncertainties are due to a lack of knowledge on the actual state of the measurement context. First we identify an explicit criterion that enables us to verify whether a given hidden measurement system is a representation of a given couple $\Si,{\cal E}$ consisting of a set of states $\Si$ and a set of measurements ${\cal E}$ ($=$ measurement system). Then we prove for every measurement system that there exists at least one representation as a hidden measurement system with $[0,1]$ as set of states of the measurement context. Thus, we can apply this definition of a hidden measurement system to impose an axiomatics for context dependence. We show that in this way we always find classical representations (hidden measurement representations) for general non-classical entities (e.g. quantum entities).
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