论文标题
古尔的定理重新审视
Gull's theorem revisited
论文作者
论文摘要
史蒂夫·古尔（Steve Gull）在他的剑桥大学主页上未发表的作品中，使用傅立叶理论概述了贝尔定理的证明。 Gull的理念是，Bell的定理（或证明中的关键引理）可以看作是使用经典而不是量子计算机进行分布式计算项目项目的无关定理。我们提出了他的论点，纠正了错误印刷和填补空白。在他的论点中，网络中有两台完全分开的计算机。我们需要三个以填补他的证明中的所有空白：第三台计算机向代表贝尔工作中两个测量站的两台计算机提供随机数。还可以想象，计算机被克隆的虚拟计算机所取代，在爱丽丝和鲍勃的计算机中生成相同的伪随机数。无论哪种方式，我们都需要假设存在共享的I.I.D. I.I.D.实现的同步序列的形式的随机性。试验序列的原本确定性物理基础的隐藏变量。然后，Gull的证明只需要第三步：重写期望作为对有条件期望的期望，鉴于隐藏的变量。
Steve Gull, in unpublished work available on his Cambridge University homepage, has outlined a proof of Bell's theorem using Fourier theory.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.
