"An important assumption going into the theorem is that neither Alice nor Bob is allowed, in any way, to affect the preparation of the initial state"
The assumption is that the past can't change the future, which it obviously can to any observer. You change what you do today and it will change the future. If the two particles are entangled, one particle would change the initial state of the other wouldn't it? Sort of a two way street/two way radio going back and forth potentially?
Seems like you'd be sending information to the future about the changes the information coming from the future was making to the past at the same time as the information from the future was making those changes, so the theory about not changing the initial state would be flawed.
The point of the no-communication theorem is that if you transport one half of the entangled pair to Alice, and one half of the entangled pair to Bob, neither of them can use measurements on their half of the entangled pair to communicate. It's forbidden by QM as we know it.
If Alice can affect the initial state, of course she can use that to communicate something to Bob, because half of that state then gets transported to Bob. That's exactly as interesting as sending a qubit to Bob in the normal way, so: not very.
> one particle would change the initial state of the other wouldn't it
It wouldn't, or at least not in any way that is accessible to Alice or Bob. If Alice or Bob pokes their particle too hard it will stop being entangled, and there's no operations you can do on one half of the pair that will communicate any information to the other half. Widely-separated entanglement has already been demonstrated, the reason nobody has been able to use it to transmit information is because it's forbidden by QM and so almost nobody has tried, and nobody expects it to work because it that's not how entanglement is understood to work.
A lot of people have a mental model that entanglement means that there's an invisible see-saw between the two particles, so if you could just force one particle to be spin-down then the other one would be spin-up, and that would let you communicate. Unfortunately, the connection is much less durable than that; interacting enough with the particle to force it into a definite state is an observation, and observing the particle cannot transmit information (that's what the no-communication theorem says).
If it does somehow work, it will be because QM is totally wrong. Also it would immediately be used to cheat the stock market.
"so almost nobody has tried, and nobody expects it to work because it that's not how entanglement is understood to work."
Thank you.
I'm thinking you have schrodinger's box, you have particles set inside it you know are all entangled with other particles in the future. You read the initial 'code'.
Can you change the particle from on/off? What happens if you eliminate a particle in the future that is entangled with a past particle/vice versa; will that particle change states or somehow escape the box?
How would you know if the code had changed? If you observed it in the past the past would have changed so it would seem like nothing had changed. Or would both the past observation and future (if possible) be changed at the same time?
So I guess what I'm asking is the theory saying it's actually impossible, or just saying we can't currently figure out a way to see it?
If the past and future changed at the same time we probably wouldn't currently be looking at that as communicated information, even if information was being communicated to the past from the future. Now what about the initial communication that changed the past? Does it even need to occur any longer once the past and future have changed, or do we just sort of slide into the new future by altering the past?
IE could you do an experiment with two boxes of quantum entangled particles, one box is read, the other box in a 'sealed room' for a set amount of time. If the entanglement through time is possible, and altering a entangled particle so it's sister particle responds is possible, would there be a chance that when you changed the entangled particle in the sealed room after it was unsealed it would change the particle in the observed room?
Or would it be like where entanglement through time may be possible, the original measurements in both boxes would change instantaneously if the 'later' box was changed so it's, as far as we know, unmeasurable?
Could you create a black box of entangled particles and a code to read them and post it and just hope someone would write to you from the future and you could read it? Sort of like Hawking's time travel party nobody showed up to but for information and just hope something shows up someday. So the code never changes, but the entangled particles in the box can. This could potentially get around the problem of not knowing if the particles were switched in the box. You know the code which doesn't change so you could simply read the box every day and hope that someone from the future had set the particles to a definite state that was readable. I understand that if the particles are observed it doesn't automatically change the particle, but if the particles are observed one way and are continuously observed then they must stay that way, and then the entangled particles must be the opposite of that. From what I understand you're saying it'd be a one and done transmission, but then it wouldn't break the no communication theorem and would be ftl (using a slower than light method, the code which would travel through time at regular speed, to jumpstart the process).
> altering a entangled particle so it's sister particle responds is possible
Altering the particle (as far as anyone knows) breaks the entanglement. The person on one end can measure their particle, but that doesn't tell them anything about whether or how the other one was altered.
Once you observe your particle, you've collapsed the wavefunction of the entangled pair. But- crucially- it's not possible to observe the wavefunction itself, so nobody else can tell whether it's collapsed. That is, if I measure my particle, I have no idea whether the particle on the other end will or has already been changed or observed, and I can't know. It just gives me a random value and collapses the state if it hasn't already.
It's only in retrospect that you can detect entanglement; the values you get upon observation of the pairs are correlated once you have both sets of values to compare. But until then you just have a bunch of white noise, and it's not possible (this is the no-communication theorem) to make any sense of that white noise.
Imagine that you have pair of socks. You sent one sock to Alice and the second sock to Bob. When Alice opened her package, she sees the left sock, so she immediately knows that Bob received the right sock. This is the FTL communication.
Alice can forcefully change her sock from left sock to right sock and back, e.g. by putting sock to the corresponding foots, but Bob will never know that.
https://en.wikipedia.org/wiki/No-communication_theorem