论文标题
模拟量子上下文的隐藏变量越来越违反了漏洞绑定
Hidden variables simulating quantum contextuality increasingly violate the Holevo bound
论文作者
论文摘要
在2011年以来的本文中，我们使用正式逻辑的工具来解决有关量子上下文的一些问题。特别是，我们考虑了与Peres-Mermin Square相关的实验。实验结果的所有可能序列的语言被归类于乔姆斯基层次结构，被视为一种常规语言。接下来，我们做出一个相当明显的观察结果，即在理想孤立的可重复实验中，一组有限的隐藏有限变量永远无法说明不确定性。我们看到，当实验可能结果的语言是规则的，就像Peres-Mermin Square一样，二进制价值的隐藏变量的量是为了使所有实验序列降低到长度n增长的序列所需的模型所需的隐藏变量量，从而可以：在n中是线性的。我们介绍了一种非常抽象的机器模型，该模型在特定意义上模拟了自然。如果要模拟与Peres-Mermin Square相对应的实验，则证明了此类机器内存状态的数量较低。此外，该下限的证据被认为是缩放到佩雷斯人正方形的一定概括。对于这个缩放的实验，可以看出漏洞结合被违反，违规程度均匀增加。
In this paper from 2011 we approach some questions about quantum contextuality with tools from formal logic. In particular, we consider an experiment associated with the Peres-Mermin square. The language of all possible sequences of outcomes of the experiment is classified in the Chomsky hierarchy and seen to be a regular language. Next, we make the rather evident observation that a finite set of hidden finite valued variables can never account for indeterminism in an ideally isolated repeatable experiment. We see that, when the language of possible outcomes of the experiment is regular, as is the case with the Peres-Mermin square, the amount of binary-valued hidden variables needed to de-randomize the model for all sequences of experiments up to length n grows as bad as it could be: linearly in n. We introduce a very abstract model of machine that simulates nature in a particular sense. A lower-bound on the number of memory states of such machines is proved if they were to simulate the experiment that corresponds to the Peres-Mermin square. Moreover, the proof of this lower bound is seen to scale to a certain generalization of the Peres- Mermin square. For this scaled experiment it is seen that the Holevo bound is violated and that the degree of violation increases uniformly.
