Related papers: Gull's theorem revisited

Gull's theorem revisited

URL: http://arxiv.org/abs/2012.00719v9
Date: Fri, 27 May 2022 08:58:19 GMT
Title: Gull's theorem revisited
Authors: Richard D. Gill
Abstract summary: Gull's philosophy is that Bell's theorem can be seen as a no-go theorem for a project in distributed computing. We present his argument, correcting misprints and filling gaps.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Steve Gull, in unpublished work available on his Cambridge University homepage, has outlined a proof of Bell's theorem using Fourier theory.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.

Related papers

A no-go theorem for sequential and retro-causal hidden-variable theories based on computational complexity [0.0]
Bell's no-go theorem requires a theory to model quantum correlation-at-a-distance phenomena. If a theory is compatible with quantum mechanics, then the problems of solving its mathematical models must be as hard as calculating the output of quantum circuits. I show that these classes fail to cover the computational complexity of sampling from quantum circuits. The result represents a no-go theorem that rules out a large family of sequential and post-selection-based theories.
arXiv Detail & Related papers (2024-09-18T08:19:58Z)
Some consequences of Sica's approach to Bell's inequalities [55.2480439325792]
Louis Sica derived Bell's inequalities from the hypothesis that the time series of outcomes observed in one station does not change if the setting in the other station is changed. In this paper, Sica's approach is extended to series with non ideal efficiency and to the actual time structure of experimental data.
arXiv Detail & Related papers (2024-03-05T13:59:52Z)
Connecting classical finite exchangeability to quantum theory [69.62715388742298]
Exchangeability is a fundamental concept in probability theory and statistics. We show how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory.
arXiv Detail & Related papers (2023-06-06T17:15:19Z)
Quantum Depth in the Random Oracle Model [57.663890114335736]
We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. For some problems, the ability to perform adaptive measurements in a single shallow quantum circuit is more useful than the ability to perform many shallow quantum circuits without adaptive measurements.
arXiv Detail & Related papers (2022-10-12T17:54:02Z)
Kupczynski's Contextual Locally Causal Probabilistic Models are constrained by Bell's theorem [0.0]
Kupczynski has argued that Bell's theorem can be circumvented if one takes correct account of contextual setting-dependent parameters describing measuring instruments. We show that this is not true. Even if one takes account of contextuality in the way he suggests, the Bell-CHSH inequality can still be derived.
arXiv Detail & Related papers (2022-08-21T17:44:30Z)
Proofs of network quantum nonlocality aided by machine learning [68.8204255655161]
We show that the family of quantum triangle distributions of [DOI40103/PhysRevLett.123.140] did not admit triangle-local models in a larger range than the original proof. We produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.
arXiv Detail & Related papers (2022-03-30T18:00:00Z)
About the description of physical reality of Bell's experiment [91.3755431537592]
A hidden variables model complying with the simplest form of Local Realism was recently introduced. It reproduces Quantum Mechanics' predictions for an even ideally perfect Bell's experiment. A new type of quantum computer does not exist yet, not even in theory.
arXiv Detail & Related papers (2021-09-06T15:55:13Z)
Three computational models and its equivalence [0.0]
The study of computability has its origin in Hilbert's conference of 1900, where an adjacent question, is to give a precise description of the notion of algorithm. We intend to fill this gap presenting the proof in a modern way, without forgetting the mathematical details.
arXiv Detail & Related papers (2020-10-26T05:55:19Z)
Non-Boolean Hidden Variables model reproduces Quantum Mechanics' predictions for Bell's experiment [91.3755431537592]
Theory aimed to violate Bell's inequalities must start by giving up Boolean logic. "Hard" problem is to predict the time values when single particles are detected. "Soft" problem is to explain the violation of Bell's inequalities within (non-Boolean) Local Realism.
arXiv Detail & Related papers (2020-05-20T21:46:35Z)
Indeterminism and Undecidability [0.0]
Chaitin's follow-up to Goedel's (first) incompleteness theorem can be proved. The main point is that Bell and others did not exploit the full empirical content of quantum mechanics.
arXiv Detail & Related papers (2020-03-07T11:06:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.