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john taylor
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Can someone please tell me(and in simple terms-like in percentages), what the maximal violations of Bell's inequality has been recorded at in actual experiments and in an ideal scenario? Thank you.
I mean it in the sense that as many loopholes are closed as possible.Nugatory said:One clarification: By "ideal", do you mean an experiment that most closely resembles the idealized model Bell analyzed in his original paper (two spin-1/2 particles in the singlet state) or those experiments that most effectively close as many loopholes as possible?
This one, from 2015: https://arxiv.org/abs/1508.05949 was discussed in several threads here when it first appeared.john taylor said:I mean it in the sense that as many loopholes are closed as possible.
So is 2.42 the maximum level of violation ?Nugatory said:This one, from 2015: https://arxiv.org/abs/1508.05949 was discussed in several threads here when it first appeared.
Using the CHSH form of the inequality, 2.42 against the classical limit of 2.0
(the link is to a preprint -as far as I know the final publication is behind a paywall)
john taylor said:So is 2.42 the maximum level of violation ?
For CHSH how large is the violation given by Tsirelson's bound? So by what margin would it theoretically be larger than 2 according to this bound?atyy said:The theoretical maximum possible in quantum theory in that situation is given by Tsirelson's bound.
https://en.wikipedia.org/wiki/Tsirelson's_bound
The theoretical maximum possible in quantum theory in other situations has interesting issues including Tsirelson's problem, which is related to MIP* = RE, on which progress seems to have been made recently.
https://en.wikipedia.org/wiki/Tsirelson's_bound#Tsirelson's_problem
https://quantumfrontiers.com/2020/03/01/the-shape-of-mip-re/
Bell's Inequality is a mathematical expression that sets a limit on the correlations between measurements of entangled quantum particles. It is important in quantum mechanics because it helps to distinguish between classical and quantum behavior, and has implications for our understanding of the nature of reality.
The concept of "maximum violation" refers to the maximum amount by which the predictions of Bell's Inequality can be violated in an experiment. This violation is a key feature of quantum mechanics and has been observed in numerous experiments, demonstrating the failure of classical theories to fully explain the behavior of entangled particles.
One example is the Aspect experiment, which used polarized photons to demonstrate a violation of Bell's Inequality. Another is the Clauser-Horne-Shimony-Holt (CHSH) experiment, which used entangled particles to show a violation of Bell's Inequality. These and other experiments have consistently shown that the predictions of quantum mechanics are in conflict with those of classical theories.
The maximum violation of Bell's Inequality has significant implications for our understanding of reality. It suggests that the classical view of a deterministic, objective reality may not be accurate at the quantum level. Instead, it supports the idea that reality is probabilistic and that our observations can affect the behavior of particles. This challenges our traditional understanding of cause and effect and raises questions about the fundamental nature of the universe.
While the maximum violation of Bell's Inequality has primarily been of interest to physicists and philosophers, it has also led to potential applications in fields such as cryptography and quantum computing. The violation of Bell's Inequality can be used to generate random numbers, which are crucial for secure communication and encryption. It also plays a role in the development of quantum computers, which have the potential to solve certain problems much faster than classical computers by taking advantage of the strange behavior of entangled particles.