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I have seen lots of videos describing quantum entanglement experiments, but I've not yet found a full video of the experiment itself, so I'm not sure what is actually physically happening during the experiment and observations.

I've also read contradictory descriptions online, some saying that measuring one set of entangled particles can via "spooky action at a distance" alter the measurements of a far away set of entangled particles. But I've also seen people basically just describe it as a correlation due to past interaction, and that you can't actually transfer information this way.

So which is it? Can you transfer information using quantum entanglement? Or is it just a "spooky correlation at a distance" in terms of particle behaviors due to interaction history, and if it's the latter, what about it this correlation that cannot be explained classically? As in the latter case, I do not follow why correlated behavior between sets of particles due to past interaction history combined with conservation laws, would violate classical physics.

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    $\begingroup$ We don't know, we have equations that describe the phenomenon clearly, but we do not fully understand what those equations mean. $\endgroup$
    – user65081
    Nov 4, 2021 at 15:49
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    $\begingroup$ We understand them enough to answer your question. Two particles being correlated from their past interaction despite neither one being in a definite state yet is new. The measurement transfers information but it's random information so it cannot be used to send a message that was planned ahead of time. $\endgroup$ Nov 4, 2021 at 16:14
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    $\begingroup$ @ConnorBehan That is your own interpretation, shared by many but not all. Actually, I never heard that a measurement transfer random information. Does this information travel at c? $\endgroup$
    – user65081
    Nov 4, 2021 at 16:44
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    $\begingroup$ Of course not... nothing is traveling. But saying this would most likely confuse someone at the OP's level. There are different interpretations of what qualifies as information which is why he's heard seemingly conflicting statements. $\endgroup$ Nov 4, 2021 at 18:29

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I've also read contradictory descriptions online, some saying that measuring one set of entangled particles can via "spooky action at a distance" alter the measurements of a far away set of entangled particles. But I've also seen people basically just describe it as a correlation due to past interaction, and that you can't actually transfer information this way. So which is it? Can you transfer information using quantum entanglement? Or is it just a "spooky correlation at a distance"

You absolutely cannot transfer information using entanglement without the aid of an external (classical or otherwise) communication channel. This is actually quite easy to prove: given any bipartite state $\rho_{AB}$ shared by "Alice" and "Bob", and any (CPTP) channel $\Phi$ performed on Bob side (note that any possible operation can be described in such a way), if no further information is provided, the information available to Alice is $$\operatorname{Tr}_B((I\otimes \Phi)\rho)=\operatorname{Tr}_B(\rho_{AB}).$$ In other words, whatever happens on Bob's side, Alice's piece of the state is unchanged.

Still, that doesn't mean that the correlations themselves aren't nonclassical. Indeed, you can prove that quantum states can result in correlations that cannot be reproduced by any sort of classical theory. This doesn't contradict the previous statement about no FTL communication. The correlations are indeed stronger than those allowed by classical physics/probability theory, but they also happen to unaccessible without comparing the measurement results. In other words, Alice and Bob might share a "stronger than classical link", and they can prove that they do, but they can only do so after comparing their measurement results. See e.g. Bell's theorem for dummies, how does it work? for further details. Does Bell's theorem imply a causal connection between the measurement outcomes? is also related.

I should also remark that what I'm addressing here is the nonlocality allowed by quantum mechanics. In the question, you mention entanglement. The two things are related but not quite the same. All entangled states can be used to observe Bell nonlocality, but there are entangled states which are not Bell nonlocal. Standard reference here is Wiseman et al. 2006, but going through this would probably be a bit much here. The two things are identical for pure states anyway. Other related posts are:

This observation about the distinction between asking about entanglement and asking about nonlocality leads me to a last point, to address the titular question:

What is it about quantum entanglement that cannot be explained classically?

The phenomenon of entanglement is what you get thinking about the more general phenomenon of quantum interference/superposition from the point of view of locality. When you start asking questions about what can be achieved thanks to superpositions that could not be achieved by means of local operations only, you end up studying entanglement.

But asking what about entanglement cannot be explained classically, to me, sounds like a question that goes beyond the specific point of view that is locality. Explaining entanglement is really the same as explaining quantum interference in general. Which is essentially the same as asking what about quantum mechanics cannot be explained classically. The answer to which is: any phenomenon that is not compatible with classical explanations. There's plenty, so this becomes a bit broad for a single post.

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  • $\begingroup$ Thanks. Is it something like, the wave functions of the particles continue to interact even after the particles separate locally, affecting the future behaviors of the particles in correlated ways that classical mechanics cannot explain? $\endgroup$
    – Tristan
    Nov 9, 2021 at 15:51
  • $\begingroup$ @Tristan it's not quite like that. You cannot simply say that the particles "continue to interact after they separate", because there is no causal relation between them. There is no information leaking from one side to the other. To all practical purposes, the "particles" are correlated, but not "linked" in the sense that you can do something to one side and have the effect "magically transported" to the other side, so I wouldn't say that they "interact". Nonetheless, they are correlated in a way that cannot be explained classically. Yes, it is weird, but that's just how it is unfortunately $\endgroup$
    – glS
    Nov 9, 2021 at 16:42
  • $\begingroup$ "You cannot simply say that the particles "continue to interact after they separate", because there is no causal relation between them." I meant, is it that the wave functions of the particles are what interact? I was asking if that is what quantum entanglement says. That after the particles have no causal relation, their wave functions are still entangled, and so they will have correlated motions that cannot be classically explained. $\endgroup$
    – Tristan
    Nov 9, 2021 at 17:49
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    $\begingroup$ I think it's not helpful to talk about particles in this context. We are talking about quantum states; these can describe the state of some particle, or whatever else. The states (equivalently, their wavefunctions) are entangled, yes. Also, they are correlated in a nonclassical way. Also, they do not interact (under the assumptions considered in this context). The usual mantra applies: correlation doesn't imply causation. Talking about "correlated motions" is dangerous: you only observe nonclassical correlations comparing local meas in different bases; these won't really look like "motions" $\endgroup$
    – glS
    Nov 9, 2021 at 17:57

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