How does quantum entanglement not imply faster than light informational transfer?

Question

Can someone explain how quantum entanglement doesn’t seem to imply faster than light informational transfer?

I keep reading that quantum entanglement does not violate relativity because of the no signalling theorem.

In physics, the no-communication theorem (also referred to as the no-signaling principle) is a no-go theorem in quantum information theory. It asserts that during the measurement of an entangled quantum state, it is impossible for one observer to transmit information to another observer, regardless of their spatial separation.

This seems to stem from the fact that Alice cannot determine her measurement on one end (since it is random), and thus can’t control what to send to Bob. But Alice knowing the measurement of one particle helps us know what the measurement of another particle by Bob, even if very far away, is. Whether or not I can actually transmit this information to a receiver like Bob on the other end doesn’t imply that the other particle isn’t affected by what happened to the nearest particle. Isn’t the latter what is more crucial, especially in a fundamental physical theory?

If one particle’s state automatically collapses the wave function and thus determines another particle’s state, how is this still not a transfer of information in a global/faster than light sense? The only way to get around this to me is to say that the wave function is not actually real or physical. But other theories, such as the PBR theorem, seem to prove that the wave function does respond to something real and can’t just be epistemic (unlike what this accepted answer and the answerer’s comments seem to imply).

From the wiki:

The Pusey–Barrett–Rudolph (PBR) theorem1 is a no-go theorem in quantum foundations due to Matthew Pusey, Jonathan Barrett, and Terry Rudolph (for whom the theorem is named) in 2012. It has particular significance for how one may interpret the nature of the quantum state.

With respect to certain realist hidden variable theories that attempt to explain the predictions of quantum mechanics, the theorem rules that pure quantum states must be "ontic" in the sense that they correspond directly to states of reality, rather than "epistemic" in the sense that they represent probabilistic or incomplete states of knowledge about reality.

So what’s actually going on here?

Answer 1

Note that the key assumption of PBR is that there actually exists an "objective physical state", namely a hidden-variable model. This is similar to the assumption of Bell's theorem, as clearly stated in the paper (page 4):

The result is in the same spirit as Bell's theorem[13], which states that no local theory can reproduce the predictions of quantum theory. Both theorems need to assume that a system has a objective physical state $\lambda$ such that probabilities for measurement outcomes depend only on $\lambda$.

In other words, the BPR theorem does not prove that "the wave function does respond to something real". It only shows that it cannot be a representation of uncertainty about a hidden-variables model, which is something we already pretty much knew from Bell's theorem.

Note that the violation of locality required from a hidden-variables model in order to be consistent with quantum mechanics, is exactly the same violation of locality associated with the faster-than-light communication that you will have to assume if you insist of assigning an objective physical reality to the wavefunction.

Answer 2

1. Your example is unrelated to entanglement. Here's another example: I tell you today that I am going to visit my doctor at 3PM tomorrow. Tomorrow at 3PM I go to the doctor and you instantly know that I am there! This story does not differ in any important way from the story you've told, it clearly involves no information transfer, and you don't need quantum mechanics to explain it.

2. In fact, the simple explanation is this: You don't know that I've followed through on my promise to visit the doctor, so you don't actually know I'm there instantly at 3PM. Likewise, when Alice makes a measurement, she cannot know what measurement Bob is making, or in fact whether he's making any measurement at all. She can only know what he promised to do the last time they communicated. So the analogy between your story and the doctor story is quite tight. You are not illustrating anything that's peculiar to entanglement, and you are not illustrating anything that's peculiar to quantum mechanics.

3. It is true that some entanglement correlations can't be explained classically (barring some very contrived stories that I'll ignore here), but you'll never be able to illustrate such correlations with a story that involves specific pre-arranged measurements on both ends. If you want to illustrate the essence of entanglement, you need a story that involves multiple possible measurements on each end.

Answer 3

The easiest way to understand this involves a couple of steps. First you have to remember that correlation in itself is a shared concept in both classical and quantum physics. A common starting point is if you take a pair of shoes and have someone randomly place them in two seperate boxes and then send the different locations, one where Alice is and one where Bob is, when Alice opens her box and sees a left shoe she instantly knows Bob has a right shoe.

Did instantaneous communication occur? No. In a classical set up, even though the shoes were put in the boxes randomly, the random outcome occured before the boxes were sent to Alice and Bob. So the state, while unknown to Alice and Bob, was already determined and thus there is no "spooky action at a distance".

In a quantum set up the situation is different because the state is not determined until Alice or Bob opens their respective boxes. This fact about quantum systems is where "spooky action at a distance" is apparent because Alice and Bob will never see 2 left shoes or 2 right shoes even though the state is unknown until one of them opens a box. Further, they will always see some combination of right and left just like the classical case.

So what to make of the "spooky action at a distance" aka "nonlocality"?

The answer lies in that we have to treat the entangled state as one object that is getting elongated as we move the boxes away from each other towards Alice and Bob respectively. So while its actual state is unknown until observation, there is no real "signaling" that is occuring.

One way to think of it is if you are able to accept the concept of Schroedinger's Cat as being both dead and alive before being observed, just imagine a case where the box the cat is in has two portals on opposite ends of the box that can be opened to see the true state of the cat. Then imagine that you connect super long fiber optic cables to the portals so that you can look down the end of the cables into the box from a very long distance. Take one cable to Alice and the other to Bob. Until one of them looks down their cable the state of the cat is still unknown. Once Alice or Bob look at the cat, the cat's state becomes determined, and once that occurs then after both have had an opportunity to look and then compare notes, they will find they always agree.

It might seem like trickery to think of the shoe case that had two objects and the cat case with one object as equivalent situations, but they are. It is the "state" that is of interest in both cases, and in both cases there are only two possible outcomes of the observation (the cat is either dead or alive for both observers, and for the shoes Alice either sees a left shoe while Bob sees right, or Alice sees right while Bob sees left), so from a quantum perspective the mathematical description of the systems are the same.

In any case, the "nonlocality" is related to the apparent "size" of the seperation which plays tricks with the mind because we are not used to thinking of objects as being as "big" as the case where two shoes are seperated by a long distance, even though its equivalent to a case where they are not.

I should further note how correlation is inviolate even though the outcome of the observation of the state is not. There is no situation where Alice will observe a live cat and Bob a dead cat (or vice versa) just as there is no case of two right or two left shoes as mentioned above. The correlation is more fundamental than the state in this regard.

Answer 4

JQK’s answer is great - +1 from me. Another way to think about it: the information of the distant particle is “stored” locally in the nearby particle, so no information transfer is needed to learn about the distant particle.

When the two particles become entangled, the correlation between them will now exist post-measurement. Then, when you measure one particle, the other particle’s state is entirely derivable from that correlation and the measured state of the nearby particle. So long as that correlation is known, you can know the state of the distant particle without having to measure it/get information from it - and if you don’t know the correlation, measuring an entangled particle is exactly the same as measuring a non-entangled one.

For the distant observer measuring the distant particle, there’s no way to tell that the entanglement collapse ever happened - for all they know, their measurement has just collapsed the state into $|1\rangle$, even if it had already been collapsed into that state by you some time ago. Then, the situation is perfectly symmetric: no information transfer needed from their POV or from yours.

Answer 5

I agree with you, there is a tendency to put the problem under the rug. There are some ways around this that avoid a connection, one is superdeterminism, which I personally dislike. Another is many worlds, that might perhaps come from a mechanism like the one proposed by Wolfram and his multiway graphs. Another, which do imply a connection without invoking superluminal speeds and that I personally find more appealing, is some connection between particles similar to a wormhole, related to the ER=EPR proposal. And I am sure there might be other good ones out there.