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Nonlinear extension of QM may lead to the 'superluminal signaling' so that it seems to violate the finite speed limit. I am wondering if it's true that in all such kind of 'superluminal' setups, entanglement plays a certain role? Or is there any 'superluminal signaling' using nonlinear QM that does not need entanglement?

If this is the case that all superluminal signaling needs entanglement somehow, then I prefer to regarding such kind of 'superluminal signaling' as faked since we can not be sure such kind of non-local signaling between entangled subsystems is really 'non-local', if entanglement is really related with the construction of spacetime as some researchers claimed. At least before we know the ground truth of their relationship, it seems not 100% safe to call it 'non-local signaling', it might be in fact local. Is this possible?

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    $\begingroup$ superluminal signaling ? Please, could you provide a link to some publication ? TY $\endgroup$
    – user46925
    Dec 24, 2015 at 15:42
  • $\begingroup$ J. Bub and A. Stairs, Quantum interactions with closed timelike curves and superluminal signaling, arXiv:1309.4751v4 $\endgroup$
    – XXDD
    Dec 24, 2015 at 15:54
  • $\begingroup$ There are no closed timelike curves in reality. You can always derive anything with logic if you start with something that's false. Physics can't save you from gigo, either. Having said that, gigo considerations can be quite useful to help with an exploration of the limits of a theoretical framework. $\endgroup$
    – CuriousOne
    Dec 24, 2015 at 19:41
  • $\begingroup$ @ CuriousOne I agree with you there we do not have a CTC now. But we can not exclude its possibility. There is also some work to simulate CTC and did find some experimental results to confirm our prediction, for example Experimental Simulation of Closed Timelike Curves $\endgroup$
    – XXDD
    Dec 25, 2015 at 1:17

2 Answers 2

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Newtonian mechanics is a setup which allows for superluminal signalling yet does not involve entanglement. The same is true for non-relatistic quantum mechanics: It also does not have any universal bound on the speed at which information is propagated, and does not require entanglement for that.

Of course, all these theories are not valid in the relativistic regime, but then again, any other extension of QM which allows for superluminal signalling is for the very least purely speculative and probably also in contradiction with something we know (or we believe in).

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    $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review $\endgroup$
    – Jon Custer
    Dec 24, 2015 at 22:53
  • $\begingroup$ @JonCuster Why does this not provide an answer to the question? The question is whether all physical setups (=theories) which allow for superluminal communication involve entanglement. This is not the case. $\endgroup$
    – Norbert Schuch
    Dec 24, 2015 at 22:57
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    $\begingroup$ The question asks about quantum systems. Newtonian mechanics lacks the whole concept of entanglement. So, your answer fails to address the question. $\endgroup$
    – Jon Custer
    Dec 24, 2015 at 22:59
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    $\begingroup$ Well, then I read the question differently then you did. But if it's about QM, it is also fine: Non-relativistic QM is perfectly fine with superluminal signalling even if no entanglement is involved. I will update the answer accordingly. $\endgroup$
    – Norbert Schuch
    Dec 24, 2015 at 23:01
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    $\begingroup$ Since entanglement based design is more popular, does this mean most people prefer entanglement based solution than other mechanisms? This observation itself says something. $\endgroup$
    – XXDD
    Dec 25, 2015 at 1:23
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Here's one way, which may or may not meet the rules you have in mind.

If you're allowed to perform post-selection, then you can communicate by post-selecting on a previously-entangled qubit containing the message you wanted to send:

Post-selection allows decohered qubits to be used

The operation of the "!Select" gate is $\begin{bmatrix} 0&0\\0&1 \end{bmatrix}$. Clearly not unitary. The $x^{\lceil t \rceil}$ gate just alternates between do-nothing and apply-NOT, so I could check that both ON and OFF could be sent. I took a screensot when it was in the do-nothing state, corresponding to sending ON (and the green ON is displaying the state of the receiver's bit).

This setup weakens the requirement from "entangled" to just "correlated". Depending on your favorite interpretation, this may or may not be satisfying (e.g. in many worlds correlation is just a kind of entanglement).

Also you may philosophically object to using quantum suicide just to send a bit of information.

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  • $\begingroup$ How do you set the qbits on the sending side ? $\endgroup$
    – user46925
    Dec 26, 2015 at 5:39
  • $\begingroup$ One could reasonably object that the receiver received the message already before it was sent. $\endgroup$
    – Norbert Schuch
    Dec 26, 2015 at 11:19
  • $\begingroup$ @igael You either post-select on it being false or on it being true. My simulator only had a post-select-on-true gate so I either hit it with an X gate or not beforehand. $\endgroup$
    – Craig Gidney
    Dec 26, 2015 at 14:42
  • $\begingroup$ @NorbertSchuch Sounds like a feature to me. $\endgroup$
    – Craig Gidney
    Dec 26, 2015 at 14:43
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    $\begingroup$ @X.Dong The synchronization issue depends on how the universe hypothetically implemented post-selection. For example, suppose the post-selection was eventually consistent and took effect only in the sender's future light cone. Although, there would be observers who saw the wrong result, those observers all get discarded eventually. The remaining observers would remember having the right result all along, and any plans based on that fact will have succeeded. Avoiding discardation would require escaping the sender's hubble horizon. $\endgroup$
    – Craig Gidney
    Dec 27, 2015 at 15:11

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