# Maximum violation of Bell's Inequalities?

• I

## Main Question or Discussion Point

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.

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Nugatory
Mentor
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?

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?
I mean it in the sense that as many loopholes are closed as possible.

Nugatory
Mentor
I mean it in the sense that as many loopholes are closed as possible.
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)

• vanhees71
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)
So is 2.42 the maximum level of violation ?

atyy
So is 2.42 the maximum level of violation ?
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/

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/
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?

Nugatory
Mentor
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?
It’s just about the first thing in the Wikipedia article @atyy linked: ##2\sqrt{2}##.

• atyy