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Apologies for the additional question on a topic that seems to be queried relatively frequently in this forum -

I was unable to find an explicit answer to this specific question in searching physics stack exchange.

My question is the question in the Title of this post, but to ask it another way:

Suppose you have two entangled particles, that you have not observed/collapsed the wave function for. My (limited) understanding is that observing one particle collapses the wave function for both particles, providing you information about the state of both particles.

If you are the observer of particle "1", and particle "2" is not observable from your locality, is an observer in the locality of particle "2" aware that the wave function has been collapsed?

Thanks in advance for any insight you can provide! I was trying to read through this post which discusses the idea that entanglement is not really an active link and this thought experiment occurred to me - if there is no "real" link between two particles as a result of entanglement, then there would not necessarily be some property of the two particles that allowed you to determine whether or not the particle was observed or not - is that right?

E.g., for the observer in the locality of particle "2", there would ultimately be no way to determine whether or not the observer of particle "1" had observed the entangled particles or not. But if this is the case, how do we know the wave function of particle "2" collapses when particle 1 is observed? I.e., if we can't tell if a particle's entangled pair has been observed or not, how do we know the wave function for that particle has been collapsed? I suspect I'm attempting to assign innacurate classical descriptions to the behavior of quantum particles, and I'm hoping someone can help articulate the inaccuracies implicit in my examples above.

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    $\begingroup$ To be short and clear: no. If you could measure that, then you could transfer information faster than light. $\endgroup$
    – Pato Galmarini
    Commented Sep 10 at 7:41
  • $\begingroup$ @PatoGalmarini That's an answer $\endgroup$
    – BioPhysicist
    Commented Sep 11 at 11:56

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No, you can't tell what has happened far away if all you have access to is the local system, even if your local system is entangled with the far-away system. This is a consequence of the "no-signalling theorem" in quantum mechanics (here is an early version of it; there are many more).

Normally this theorem is considered in the context of "can you tell which distant measurement has been made?" by only looking at the local system. The answer there is clearly "no!" (the reduced local density matrix is unchanged no matter what distant measurement setting was used). But you are asking a slightly different question, comparing a distant measurement to no measurement at all. But the theorem goes through the same way; not only can't you tell which measurement was made on a distant entangled particle, you can't even tell if a measurement was made. (If the answer to this question were any different, then I suppose this would allow one to signal faster than light.)

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  • $\begingroup$ Thanks so much! Any chance there's a layman's way to describe how entanglement is experimentally verified? I think this is the piece that I keep struggling with. Is it just the wave function that we describing as entangled? $\endgroup$
    – usernamedgreg
    Commented Sep 10 at 11:49
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    $\begingroup$ @usernamedgreg Sure: Entanglement produces a variety of statistical correlations that cannot otherwise appear. If 2 particles are spin entangled, for example, they must both have their spins measured and compared. There are a variety of techniques and statistics, which vary according to the specific experiment and particle types. These aren't all easily described in lay terms, however. A common statistical test is the CHSH inequality, you can Google it to learn more. FYI: 2 entangled particles are described by a single wavefunction. It is a system of 2 particles, and not 2 independent systems. $\endgroup$
    – DrChinese
    Commented Sep 10 at 20:21
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Any time you make a quantum observation, the wave function of your system collapses in the sense that it gets projected onto the eigenspace of your observable that corresponds to the observed outcome. So if you know the outcome of your observation then you know that the wave function has collapsed, and you know what it has collapsed to.

In the case of a two-particle system and an observation made on particle 1 only --- and if the outcome of that observation corresponds to a one-dimensional eigenspace of particle 1's state space --- then it's easy to see that the newly collapsed wave function can't be entangled.

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  • $\begingroup$ Thank you! If I'm interpreting your response correctly, my scenario is not practical because of the distinctly separate observations of one particle vs the other - I'm looking at news articles like the below, how do you observe two particles simultaneously when they are 1200 kilometers apart? science.org/content/article/…. $\endgroup$
    – usernamedgreg
    Commented Sep 10 at 1:51
  • $\begingroup$ I see now that I misread the question. You asked if an observer in the vicinity of Particle 2 is aware of the collapse, and I read you as asking if an observer in the vicinity of Particle 1 is aware of the collapse. So the above is the correct answer to a question you didn't ask. Fortunately @KenWharton was a more careful reader than I and answered your actual question. $\endgroup$
    – WillO
    Commented Sep 10 at 10:29
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First, a discussion of collapse. The motion of a quantum system in general depends on what happens to all of its possible states, e.g. - during a single particle interference experiment, all of the possible paths for the particle contribute to the final outcome, see Section 2 of this paper for an example:

https://arxiv.org/abs/math/9911150

After you have done an experiment you only see one of the possible outcomes not all of them. Also, when you walk through a doorway there are multiple paths you could have taken but you don't have to worry that you're doing to diffract through the doorway. How can this be true if there are multiple versions of every system? Some physicists tried to explain this by postulating that all of the possible states except for one disappear. This is called collapse, but it doesn't actually appear in the equations of motion of quantum theory. But when information is copied out of a quantum system interference is suppressed: this is called decoherence:

https://arxiv.org/abs/1911.06282

So collapse isn't necessary to explain the fact that you only see one version of each measurement outcome and I will assume it doesn't happen for the rest of this answer. In quantum theory without collapse on a macroscopic scale in everyday life because of decoherence the different versions of systems sort themselves into layers that act like a collection of parallel universes obeying classical physics to a good but not perfect approximation:

https://arxiv.org/abs/1111.2189

https://arxiv.org/abs/quant-ph/0104033

The equations of motion of real quantum systems are local: the only way for one quantum system to influence another is for the relevant information to pass through the space between them. A measurement is just an interaction that produces a record of some property of a system and as such a measurement only changes the measured system and the measurement device and any systems they interact with.

The same is true for entangled particles. The correlations in Bell experiments don't arise from collapse. Rather, each quantum system carries information about the systems it interacted with in the past. Sometimes the quantum information that one system has about another doesn't affect the results of measurements on that system alone: locally inaccessible information. As a result that quantum information isn't destroyed by decoherence and it can be carried in classical channels. That is what happens in entanglement experiments:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

The correlations between the measurement results on entangled systems are established when the results from the two systems interact with one another after being carried in "classical" systems. This is one type of situation in which the parallel universe approximation fails.

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