Gamification of Bell's Theorem

This video shows a gamified version of Bell's Theorem called the "CHSH Game".

The theorem proves the non-local nature of quantum physics, known sometimes as "Spooky action at a distance". The gamified version further shows that quantum entanglement can be useful.

See more about the usefulness of quantum entanglement in this video about the relation of such games and interactive proofs, and a recent result related to the halting problem:

Some history:
Bell's Theorem is due to John Stuart Bell in 1964.
The CHSH inequality, by John Clauser, Michael Horne, Abner Shimony, and Richard Holt, improved on it in 1969.
The CHSH game by R. Cleve, P. Hoyer, B. Toner and J. Watrous in 2004.

About "Bell Locality":
The formal statement of it is this requirement of the probability distribution:
P(x,y|a,b,particle1,particle2)=P(x|a,particle1)P(y|b,particle2)
This means that the outcomes are independent given the input bits and the respective particle statements.
Another way to say that is as stated in the video: that given the particle the top player has, we can specify the table P(x|a,particle1), and it makes no difference what happens with the bottom player (or the other way around of course).
Bell's theorem proves this is not what's happening.

As stated in the closing slide, this conclusion relies on a few more background assumptions:
* Each measurement has one outcome. According to the "many-worlds" theory a measurement can have multiple outcomes, and Bell locallity may still hold with this interpretation.
* The referee can choose random bits. According to "superdeterminisim" world view, there's no such thing as randomness, and it might be that the referee chooses bits somehow pre-determined to match the particles held by the players.

Some more links:

Chapters:
0:00 Part 1: Decision problems
1:56 Part 2: Classical bound
6:20 Part 3: Quantum spin
13:44 Part 4: A Quantum Strategy
16:10 Part 5: Local realism
18:48 Part 6: No signaling
22:45 Part 7: Bell locality

[ThreeEarRabbit]

6:10 that escalated quickly. If coins and dice don't work, try ENTANGLED PARTICLES.
Seriously though, this was a very clear and well done video.

[najwan]

the whiplash i got when you went from coins to using quantum physics to decide which strategy to use is indescribable
well done

[i_teleported_bread]

It's nice to see udiprod is back. Their videos explaining the difference between the different types of sorting algorithms were very enlightening.

[julianatlas]

6:08 "it seems there is nothing we can do to get better performance" ok reasonable
"so let's give the player entangled particles and see what happens" well, that escalated quickly :0

[ucasvb]

Some technical remarks for those interested: There's some really deep and fascinating amount of physics and philosophy about this stuff! The "magical non-signaling box" is known as Popescu-Rohrlich boxes, if anyone wants to look it up. It's basically just a probability distribution p(a, b|x, y) (probability of a, b outcomes given x, y inputs/settings) which are non-local, but also obey non-signaling conditions. The values of x/a and y/b are assumed to be in "separate laboratories".

We say a probability distribution is local if it can be written as a probabilistic mixture of local probability distributions. Mathematically: p(a, b|x, y) = Σ_i pᵢ p(a|x, i) p(b|y, i), where pᵢ is a probability, and p(a|x, i) and p(b|y, i) are the local distributions depending on this i variable. Σ_i is "sum over the values of i". Classical physics restricts us to these.

A probability distribution is non-signaling if the outputs of one side don't depend on the inputs and outputs on the other, that is, if you compute the marginal (sum over "the other side"), you get a distribution that can be written as: p(a|x) = Σ_b p(a, b|x, y), for all a, x, y and similarly for the other side: p(b|y) = Σ_a p(a, b|x, y), for all b, x, y. This means the local probability distributions carry no information "coming from the other side".

So the distributions of these "magical non-signaling boxes" (or "PR boxes") is non-local, but it's still non-signaling. That's a VERY surprising result, because we sort of hoped that non-signaling was a property of locality, that is, non-signaling is a physical consequence of a finite speed of light. But what the (mathematical) existence of PR boxes show is that non-signaling is an independent property of locality, so we currently have no physical argument to deny the existence of such weird things.

(Mathematically, what all of these results show is that: Local Correlations ⊂ Quantum Correlations ⊂ Non-Signaling Correlations, where ⊂ denotes a strict subset.)

[lemonice]

udiprod is probably my favorite underrated channel about computer science and physics

[Bencurlis]

This is a great video!
There is still a third hidden assumption regarding Bell's theorem, in the particular case of the video, it is that input bits from the referee are uncorrelated from from the particle outcome. So, from a physical point of view, it is possible to imagine local and deterministic strategies that should still be coherent with the 85% winning quantum strategy observation, granted this correlation exists and originates in the common past of all the matter composing the game elements. This possibility is defended by Gerard 't Hooft, among others.

[tsgv]

6:10

I got so excited the moment you brought this out. That came outta nowhere.

[thomaskaldahl]

I like how you represented a biased coin by bending it :D

[LukePalmer]

Thanks, very clear, and (though occasionally tedious) I like the way you really consider all the possibilities deeply instead of handwaving, and feel I have a more solid understanding because of it.

[ronidaffan]

The most comprehensive explanation of Bell's Theorem by far. Well done !!!!

[robotspark]

The video is incredible, but udiprod has gone above and beyond in responding to people's questions and queries about such a hard to grasp subject (even with a very helpful video such as this) :)

[henke]

Always nice to see another video, you guys have such incredible clarity when explaining things. Here's a topic suggestion: the pigeon hole principle and what it means for compression.

[iamagreatape]

i just watched a whole video on quantum computing, understood none of it, but still was invested through the whole thing anyways.

[TheRenaSystem]

Great to see you're still on the platform! The last video I watched of yours was one about sorting algorithms from a few years back, so it's cool to see you still here and making content, great stuff!

[BurnerWah]

This channel is cool
I started out wanting to see bogosort and now I'm learning physics

[idnrzpu]

It's weird how the universe cares specifically about whether it's communication or not.
We found this "quantum" thing that makes something instant and tried so hard with it. Yet the universe said "nope." therefore we can't send information with it.

[kinghotcoc]

Once again another lovely udiprod video, while they do take a while to post, the quality is always amazing.

[punpumpkin]

I don’t know much about physics, but this is still very entertaining. I am happy this was on my recommended.

[doBobro]

Thank you! I've always been struggling with bell theorem before your explanation. Finally it clicked!