Question about Bell's inequalities and 3-particle entanglement

[Isaac Hart]

Could someone please clarify a question that I had? Is it true that 3 or more electrons/particles can be described under one wavefunction, making them entangled? If so, could you use Bell's principles of the comparison of their states like their spin, polarization or position to see if two out of the three electrons are entangled? If I were to label all three as A, B and C could you use Bell inequalities to detect whether they are entangled without the need of electron C? Only comparing the states of A and B to see whether they are still entangled or not.

Quite a random question, I know.

Thanks, Isaac.

 

[DrChinese]

Could someone please clarify a question that I had? Is it true that 3 or more electrons/particles can be described under one wavefunction, making them entangled? If so, could you use Bell's principles of the comparison of their states like their spin, polarization or position to see if two out of the three electrons are entangled? If I were to label all three as A, B and C could you use Bell inequalities to detect whether they are entangled without the need of electron C? Only comparing the states of A and B to see whether they are still entangled or not.

Three photon entanglement has been explored extensively in both theory and experiment over the past 35 years. There are 2 primary states that are usually discussed: the GHZ state |000>+|111> and the W state |100>+|010>+|001>. Both of these allow for maximal entanglement.

HOWEVER: The rules relating to pairs of these are fairly complicated, and does not at all work as you might expect. Further: N=3 is not the limit for maximal entanglement, and the rules get exponentially more complex as N increases.

To answer your question more specifically: There are no tests that can be run on A and B to determine of C has already been measured or not. That's because the order of measurement has no observable effect on entangled statistics. Only the final context need be considered (i.e. how each of A, B and C are measured).

Check out for example: Greenberger–Horne–Zeilinger state

 

[Vanadium 50]

If I were to label all three as A, B and C

You cannot. You cannot say "this electron is doing this". At best you can say "I detected an electron doing this".

Quite a random question, I know.

@PeterDonis warned you that this is an ineffective way to learn way back on...Tuesday. I know that was a long time ago, but it is still true.

Do you paint your house by firing paintballs in random directions?

 

[Nugatory]

If I were to label all three as A, B and C could you use Bell inequalities to detect whether they are entangled without the need of electron C?

Bell inequalities are not how we detect entanglement, whether working with two particle systems or more complicated ones.

 

[Isaac Hart]

Thank you DrChinese, that has put an end to my little train of thought. I greatly appreciate the clarification on This thread. I hope to see the day that someone knocks down that pesty no-signalling theorem. =)

 

[Isaac Hart]

You cannot. You cannot say "this electron is doing this". At best you can say "I detected an electron doing this".


@PeterDonis warned you that this is an ineffective way to learn way back on...Tuesday. I know that was a long time ago, but it is still true.

Do you paint your house by firing paintballs in random directions?

Why certainly, everything is chaotic in a way. Painting a house with paintballs would certainly be an interesting way of going about it. It people that take the most interesting routes who find success in their fields of work, I hope to be one of them.

Have a nice day, Vanadium 50. =)

 

[Isaac Hart]

Bell inequalities are not how we detect entanglement, whether working with two particle systems or more complicated ones.

Bell's theorem, proposed by physicist John S. Bell in 1964, states that no physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics. This theorem leads to Bell's inequalities, which are mathematical inequalities that must be satisfied by any local hidden variable theory.

You can use Experimental Tests: To test Bell's inequalities, experiments are performed where entangled particles are measured in different settings. The results are then compared to the limits set by Bell's inequalities. Consistent violation of these inequalities in numerous experiments supports the existence of entanglement.

Thanks you for the feedback Nugatory, however, I thought Bell's inequalities are exactly the methods scientists use to detect entanglement. Please correct me if I am wrong.

Have a nice day =)

 

[PeterDonis]

I thought Bell's inequalities are exactly the methods scientists use to detect entanglement. Please correct me if I am wrong.

You are wrong. You should be able to tell that from what you yourself said about them:

Bell's theorem, proposed by physicist John S. Bell in 1964, states that no physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics.

That's a consequence of the theorem, but it's not what the theorem itself states. The theorem itself states that theories meeting certain specifications, which Bell calls "local hidden variable theories", can only make predictions that satisfy the Bell inequalities.

This theorem leads to Bell's inequalities, which are mathematical inequalities that must be satisfied by any local hidden variable theory.

In other words, Bell's theorem and the Bell inequalities have nothing to do with entanglement in quantum mechanics. They are about "local hidden variable theories", which QM is not, since QM's predictions violate the Bell inequalities. But that's all that Bell inequality violations tell you. They tell you nothing about the actual quantum state of the particles being experimented on.

Consistent violation of these inequalities in numerous experiments supports the existence of entanglement.

No, it doesn't. All it tells you is that any theory that can correctly predict those experimental results cannot be a local hidden variable theory. See above, and think carefully about the logic.

 

[Vanadium 50]

You are wrong.

Well, technically his AI is wrong. The text was AI-generated.

It's a pity he's rejected the advice to start at the beginning and work to the end. As it is, he seems to know two things and thus thinks they must be connected. However, as you point out, they are really different things. Further, this thread suffers from two additional misconceptions - one is that entangling two particles is hard to understand because its just not complicated enough, and the other is that electrons are distinguishable. Both would be fixed by starting at the beginning and working towards the end.

 

[Nugatory]

It people that take the most interesting routes who find success in their fields of work, I hope to be one of them.

However your chances of finding any route, whether interesting or not, are near-zero if you do not know the starting point and the destination. Bluntly, what you are doing now is about as likely to be effective as trying to revolutionize ichthyology based on what you might learn from Dr. Seuss’s classic text “One Fish, Two Fish, Red Fish, Blue Fish”.

That may be sound harsh, but in fact it is wildly good news: A few years of disciplined study and you can own knowledge that was developed over several centuries by some of the smartest people who ever lived. But it’s on you to decide if that’s what you want….

 

[Nugatory]

The text was AI-generated.

Hmmm…. Getting different results from different chatbot detectors on this text, so will remind @Isaac Hart of the forum rules:

Posting AI-generated text without attribution is categorically disallowed and will lead to a warning and an eventual permanent ban with continued use.

(And @Isaac Hart trying to understand physics by interacting with a chatbot is a complete waste of time).

 

[Vanadium 50]

(And @Isaac Hart trying to understand physics by interacting with a chatbot is a complete waste of time).

True that. It's probably worse than nothing, as it has no understanding of the right answer and will likely simply repeat others' misconceptions.

But the real lesson is start at the beginning. If you want to discuss multiparticle wavefunctions, you need to get to multiparticle wavefunctions. Peter is right here.

 

[EDMM2]

I can't believe you are using "chatbot" (AI?) text detectors.

They're all full of dang.

 

[Nugatory]

I can't believe you are using "chatbot" (AI?) text detectors.

We aren't, precisely because (as here) they are so unreliable.

 

[Isaac Hart]

You are wrong. You should be able to tell that from what you yourself said about them:


That's a consequence of the theorem, but it's not what the theorem itself states. The theorem itself states that theories meeting certain specifications, which Bell calls "local hidden variable theories", can only make predictions that satisfy the Bell inequalities.


In other words, Bell's theorem and the Bell inequalities have nothing to do with entanglement in quantum mechanics. They are about "local hidden variable theories", which QM is not, since QM's predictions violate the Bell inequalities. But that's all that Bell inequality violations tell you. They tell you nothing about the actual quantum state of the particles being experimented on.


No, it doesn't. All it tells you is that any theory that can correctly predict those experimental results cannot be a local hidden variable theory. See above, and think carefully about the logic.

Oh, my bad. Again thank you very much for clearing that point. Although you said that this is not a good way to learn, I have learnt a great deal, I won't post anything for a weak and when I do it will be less nonsense than I have posted here.