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I'm referring to this recent paper, "Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurements" by Fuwa et al. published in Nature Communications. Non-paywalled arXiv version here. From the abstract:

...the choice of measurement in one lab really causes a change in the local quantum state in the other lab

My understanding of entanglement (whether it is two particles, or one as in this article) is that Bob's measurement can be affected by the (uncontrollable) result of Alice's measurement, but not her choice of measurement. (the latter would seem to enable a form of non-local communication). So is it just a badly-worded abstract? (the full article uses similar language)

Hugh Allen
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From my initial reading of the paper it looks like the the quantum state Bob has access to is changed by Alice's choice of measurement but in such a way that he can't tell until Alice communicates her choice of measurement to him.

In particular they present a way for Alice to prove to Bob that she has influenced the part of the state he has access to even if he doesn't trust her (so even if Alice is malicious Bob can be confident that they shared an entangled state initially).

The phase that Bob measures looks to be uniformly distributed if he doesn't condition on anything. However if he conditions his measurements on the numbers Alice gives him (basically he splits the data up into groups depending on what settings Alice says she chose) structure emerges as shown in figure 2.

This is quite a general feature of entanglement. Alice can "steer" the quantum state Bob has access to in what appears to be a violation of special relativity but only in such a way that Bob can't tell unless Alice sends him supplementary information over a classical channel (so they can't break causality).

I agree that there is a huge amount of superstition / misinformation around about quantum effects though (especially entanglement effects).

or1426
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  • I'm trying to understand this but it makes no sense. What they are arguing is that it's a non-local effect, i.e. that something Alice does affects Bob's measurement. However I don't see why that is non-local, because if Alice has to tell Bob she did something (using non-FTL communications), then clearly, there has been time for the effect of her measurement upon the wavefunction to propagate over to Bob's lab, where it is now local. It's like throwing a rock in a pond, then waiting for the waves of your rock to get to the other side, and saying, "look at my waves." How is that non-local? – CommaToast Apr 03 '15 at 00:37
  • @CommaToast Her and Bob's measurements are time like separated which means nothing causal (slower than light) can transfer information between them. Bob initially gains results which look random. Then Alice sends over her information and Bob splits his results into bins depending on the settings Alice chose which reveals the structure.

    So the structure was always in Bob's data but he didn't know how to see it until Alice sends her causal message.

     – or1426 Apr 03 '15 at 11:17
  • Ok, I think I'm following. So, forgetting about any "communication" between the two observers, but just looking at the order in which they make their observations: does Alice take her actual measurements prior to Bob taking his actual measurements? Or is it that Bob takes his measurement prior to Alice taking hers? Are they in different buildings with different electrical power systems? Is there any shielding that would block interference from Alice's apparatus from affecting Bob's? Just trying to understand. – CommaToast Apr 04 '15 at 17:41
  • @CommaToast Alice is making her measurements before Bob making his. The entire thing takes place in one lab in this experiment but its set up so there is nothing communicated from Alice to Bob that would interfere.

    In principle you could do the experiment with different labs on different planets if you liked and the result would be the same.

    The important thing is that the result they measure is exactly what we expect from quantum mechanics (its what the theory predicts) so people aren't really looking for alternative explanations to do with the power systems or whatever.

     – or1426 Apr 04 '15 at 22:29
  • I'm just trying to understand how the experiment works, as I'm new to all this. They shoot a stream of single photons at 8000 per second through a beamsplitter and Alice measures each photon before Bob does. How does she have time to measure it before Bob? What is Bob measuring, when the photon goes to Alice instead of to him? Also am I understanding correctly that (in layman's terms) the theta of Alice's homodyne detector affects the total number of photons that Bob detects by changing the probability that he'll detect one? Or does it just change a property of the photons he detects? – CommaToast Apr 05 '15 at 18:46
  • @CommaToast I'm not entirely sure what you mean by "How does she have the time...". Could you explain that?

    After going through the beam splitter the photon is in a superposition of going to Alice and to Bob. There isn't really any classical intuition that can help here except to say that quantum things can be in two places at the same time. It isn't accurate to say the photon goes to either Alice or Bob. In all cases it goes to both.

    The theta Alice chooses affects a property of the photons which Bob can measure.

     – or1426 Apr 05 '15 at 22:54
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    I've read the study, I know what they are saying happens. However, what's not clear to me is how they know it's not light pollution feeding back upstream from Alice to Bob that's causing the shift. I mean, it's not like they're able to do the experiment on a single photon. They need to leave the laser turned on for a significant time and average their readings out over many photons. Sometimes effects are just artifacts of lab environments. And if every similar such experiment ever done was in such an environment, then it's a self-reinforcing prophesy. – CommaToast Apr 10 '15 at 03:48
  • @CommaToast: Well the "prophecy" was made in the 1920s and has successfully explained many phenomena including entanglement and superposition in single electrons as well as photons.

    Its hard at this point to argue that much of quantum mechanics hasn't been tested rigorously.

     – or1426 Apr 10 '15 at 18:34
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    Oh, I have no doubts as to QM's accuracy. I just want to know what is causing this effect. Saying Alice's measurement causes it does not explain how it does. – CommaToast Apr 14 '15 at 07:09
  • @CommaToast. I don't think there's a nice way to explain it unless you're familiar with the maths of quantum mechanics. Basically we say "Alice's measurement does this because the Born law works." and that's the best we can currently do. We don't have any classical intuition as to why. There are attempts to derive the Born law from the rest of quantum mechanics. I think the many worlds interpretation can do it in although there are some technical issues with the proof (it only works for rational probabilities for a start). – or1426 Apr 14 '15 at 11:56