Bell’s theorem as a no-go result in classical distributed Monte-Carlo simulation

Abstract and slides of a talk to be given at the IMS conference in London, 27–30 June 2022,

It has long been realized that the mathematical core of Bell’s theorem is essentially a classical probabilistic proof that a certain distributed computing task is impossible: namely, the Monte Carlo simulation of certain iconic quantum correlations. I will present a new and simple proof of the theorem using Fourier methods (time series analysis) which should appeal to probabilists and statisticians. I call it Gull’s theorem since it was sketched in a conference talk many years ago by astrophysicist Steve Gull, but never published. Indeed, there was a gap in the proof.

The connection with the topic of this session [IS18 – Quantum Computing and Statistics – organiser Yazhen Wang, University of Wisconsin-Madison] is the following: though a useful quantum computer is perhaps still a dream, many believe that a useful quantum internet is very close indeed. The first application will be: creating shared secret random cryptographic keys which, due to the laws of physics, cannot possibly be known to any other agent. So-called loophole-free Bell experiments have already been used for this purpose. 

Like other proofs of Bell’s theorem, the proof concerns a thought experiment, and the thought experiment could also in principle be carried out in the lab. This connects to the concept of functional Bell inequalities, whose application in the quantum research lab has not yet been explored. This is again a task for classical statisticians to explore.
R.D. Gill (2022) Gull’s theorem revisited, Entropy 2022, 24(5), 679 (11pp.)

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