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Gull’s Theorem Revisited

Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Academic Editors: Durdu Guney and David Petrosyan
Entropy 2022, 24(5), 679; https://doi.org/10.3390/e24050679
Received: 25 March 2022 / Revised: 2 May 2022 / Accepted: 6 May 2022 / Published: 11 May 2022
(This article belongs to the Topic Quantum Information and Quantum Computing)
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. View Full-Text
Keywords: Bell’s theorem; quantum entanglement; Monte Carlo simulation; singlet correlations; EPR-B model; local realism; quantum foundations Bell’s theorem; quantum entanglement; Monte Carlo simulation; singlet correlations; EPR-B model; local realism; quantum foundations
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MDPI and ACS Style

Gill, R.D. Gull’s Theorem Revisited. Entropy 2022, 24, 679. https://doi.org/10.3390/e24050679

AMA Style

Gill RD. Gull’s Theorem Revisited. Entropy. 2022; 24(5):679. https://doi.org/10.3390/e24050679

Chicago/Turabian Style

Gill, Richard D. 2022. "Gull’s Theorem Revisited" Entropy 24, no. 5: 679. https://doi.org/10.3390/e24050679

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