Gill Richard D
Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.
Entropy (Basel). 2022 May 11;24(5):679. doi: 10.3390/e24050679.
In 2016, Steve Gull has outlined has outlined a proof of Bell's theorem using Fourier theory. Gull's philosophy is that Bell's theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell's work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob's computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull's proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables.
2016年，史蒂夫·古尔（Steve Gull）利用傅里叶理论概述了贝尔定理的一个证明。古尔的观点是，贝尔定理（或者其证明中的一个关键引理）可以被视为一个关于使用经典计算机而非量子计算机进行分布式计算项目的不可能定理。我们展示他的论证，纠正印刷错误并填补空白。在他的论证中，网络中有两台完全分离的计算机。为了填补他证明中的所有空白，我们需要三台：第三台计算机为代表贝尔实验中两个测量站的两台计算机提供随机数流。也可以想象这台计算机被一台克隆的虚拟计算机取代，在爱丽丝和鲍勃各自的计算机中生成相同的伪随机数。不管怎样，我们需要一个假设，即存在以独立同分布隐藏变量实现的同步序列形式存在的共享独立同分布随机性，这些隐藏变量是试验序列的确定性物理过程的基础。然后，古尔的证明只需要第三步：将一个期望重写为给定隐藏变量的条件期望的期望。
