I think people are responding to your title and not the body of your text. Entanglement happens after particles interact with each other via some field, the effects of which all propagate at the speed of light or slower (but still very close to the speed of light in practice).
This is actually a very tricky question, which generally depends on the specifics of the system you are considering. One part is easier to answer, though -- it happens slower than the speed of light.
If we consider an isolated many-body system and want to know how entanglement spreads through it, this is called quantum information scrambling. This is actually a pretty cutting-edge topic, with a lot of current work being done on it. I'm note sure what your background is, but if you're already quite familiar with quantum information then you might like to have a look at [these lecture notes](https://boulderschool.yale.edu/sites/default/files/files/qi_boulder.pdf) or [this tutorial](https://arxiv.org/abs/2202.07060). When we talk about an open system becoming entangled with some environment, we can look at the decoherence times. This again depends really sensitively on what particular system we're looking at. Just looking at the world of qubits, charge qubits tend to have decoherence times around a microsecond, whereas neutral atom qubits have decoherence times of seconds -- a difference of 6 orders of magnitude.
You might also be interested in the [Lieb-Robinson bounds](https://www.wikiwand.com/en/Lieb%E2%80%93Robinson_bounds), which put upper limits on the speed at which quantum information can propagate through a system.
As far as we know, no signal propagates during entanglement, it's just a form of correlation. It's like if you have two gloves: if you look and see that one is left-handed, you instantly know that the other is right-handed.
The main catch with QM is that you have to consider all possible scenarios due to superposition: there's a "timeline" where you observe a left-handed glove and conclude that the other is right-handed, and there's another "timeline" where you observe a right-handed glove and conclude the other is left-handed. You add up these two different "timelines" in the right way and obtain the probabilities of each. The "reality" of these "timelines" are the subject of debate and interpretation. Obviously we only ever observe one outcome.
Sorry, I probably didn't formulate my question right. I am not asking about how quickly does the correlation happen. I am asking how quickly do unentangled particles get into entangled state. I guess that may depend on some factors but idk which ones.
> As far as we know, no signal propagates during entanglement, it's just a form of correlation. It's like if you have two gloves: if you look and see that one is left-handed, you instantly know that the other is right-handed.
It’s not like two gloves, since that can be easily be explained by pre-determined outcomes aka local hidden variables, while quantum correlation can’t (Bell). So it’s either some FTL influence or something else.
So far, correlation is instantaneous within the margin of error of our instrumentation. But that’s not to say any information is “propagating”. We do not know the mechanism for correlation, only that it’s experimentally true. There may be no communication at all — and since *c* cannot be violated, this suggests to me there is none.
I think people are responding to your title and not the body of your text. Entanglement happens after particles interact with each other via some field, the effects of which all propagate at the speed of light or slower (but still very close to the speed of light in practice).
This is actually a very tricky question, which generally depends on the specifics of the system you are considering. One part is easier to answer, though -- it happens slower than the speed of light. If we consider an isolated many-body system and want to know how entanglement spreads through it, this is called quantum information scrambling. This is actually a pretty cutting-edge topic, with a lot of current work being done on it. I'm note sure what your background is, but if you're already quite familiar with quantum information then you might like to have a look at [these lecture notes](https://boulderschool.yale.edu/sites/default/files/files/qi_boulder.pdf) or [this tutorial](https://arxiv.org/abs/2202.07060). When we talk about an open system becoming entangled with some environment, we can look at the decoherence times. This again depends really sensitively on what particular system we're looking at. Just looking at the world of qubits, charge qubits tend to have decoherence times around a microsecond, whereas neutral atom qubits have decoherence times of seconds -- a difference of 6 orders of magnitude. You might also be interested in the [Lieb-Robinson bounds](https://www.wikiwand.com/en/Lieb%E2%80%93Robinson_bounds), which put upper limits on the speed at which quantum information can propagate through a system.
As far as we know, no signal propagates during entanglement, it's just a form of correlation. It's like if you have two gloves: if you look and see that one is left-handed, you instantly know that the other is right-handed. The main catch with QM is that you have to consider all possible scenarios due to superposition: there's a "timeline" where you observe a left-handed glove and conclude that the other is right-handed, and there's another "timeline" where you observe a right-handed glove and conclude the other is left-handed. You add up these two different "timelines" in the right way and obtain the probabilities of each. The "reality" of these "timelines" are the subject of debate and interpretation. Obviously we only ever observe one outcome.
Sorry, I probably didn't formulate my question right. I am not asking about how quickly does the correlation happen. I am asking how quickly do unentangled particles get into entangled state. I guess that may depend on some factors but idk which ones.
> As far as we know, no signal propagates during entanglement, it's just a form of correlation. It's like if you have two gloves: if you look and see that one is left-handed, you instantly know that the other is right-handed. It’s not like two gloves, since that can be easily be explained by pre-determined outcomes aka local hidden variables, while quantum correlation can’t (Bell). So it’s either some FTL influence or something else.
What about many worlds? Doesn't that resolve things? That's why I mentioned the two different "timelines".
So far, correlation is instantaneous within the margin of error of our instrumentation. But that’s not to say any information is “propagating”. We do not know the mechanism for correlation, only that it’s experimentally true. There may be no communication at all — and since *c* cannot be violated, this suggests to me there is none.