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In a philosophically rather interesting experiment, Ma et al. show that backward causality exists in quantum physics. An Ars Technnica-article gives a less technical account.

From Ars Technica:

Delayed-choice entanglement swapping consists of the following steps. (I use the same names for the fictional experimenters as in the paper for convenience, but note that they represent acts of measurement, not literal people.)

  • Two independent sources (labeled I and II) produce pairs photons such that their polarization states are entangled. One photon from I goes to Alice, while one photon from II is sent to Bob. The second photon from each source goes to Victor. (I'm not sure why the third party is named "Victor".)

  • Alice and Bob independently perform polarization measurements; no communication passes between them during the experiment—they set the orientation of their polarization filters without knowing what the other is doing.

  • At some time after Alice and Bob perform their measurements, Victor makes a choice (the "delayed choice" in the name). He either allows his two photons from I and II to travel on without doing anything, or he combines them so that their polarization states are entangled. A final measurement determines the polarization state of those two photons.

The results of all four measurements are then compared. If Victor did not entangle his two photons, the photons received by Alice and Bob are uncorrelated with each other: the outcome of their measurements are consistent with random chance. (This is the "entanglement swapping" portion of the name.) If Victor entangled the photons, then Alice and Bob's photons have correlated polarizations—even though they were not part of the same system and never interacted.

Now, this is rather interesting in itself. My interpretation is that the universe already "knows" whether Victor will entangle or not at the time of Alice's and Bob's measurements (since it controls Victor's random generator). This kind of avoids the paradox.

The real interesting question, however, is why they haven't designed the experiment in the following way:

Instead of letting Victor randomize whether to entangle, he should base his decision on the measurements of Alice and Bob: if they measured correlated polarizations, he should not entangle; if they measured uncorrelated polarizations, he should entangle.

Seemingly, this would force the universe to produce correlated polarizations for Alice and Bob, despite there being no entanglement-chain connecting them. (Because, clearly, it would be contradictory if they were uncorrelated, despite there being a chain connecting them.)

To me, this seems like a more interesting experiment/result. Any idea why they didn't do it this way?

Update to answer @Nathaniel's comment: I don't think several measurements is necessary. Let's say that both Alice and Bob check for horizontal polarization: then if Victor decides to entangle, both Alice and Bob must get the same outcome (either fire, or don't fire). Obviously, it is not contradictory that they both get the same outcome even if there's no chain, but the experiment I'm suggesting would imply that they would always get the same outcome, despite there never being any chain.

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  • $\begingroup$ Related: physics.stackexchange.com/q/22717/2451 and physics.stackexchange.com/q/24760/2451 $\endgroup$
    – Qmechanic ♦
    May 6, 2012 at 16:13
  • $\begingroup$ Incidentally, I've been wondering about the exact same question :) $\endgroup$
    – Speldosa
    May 6, 2012 at 16:16
  • $\begingroup$ Chad Orzel gives a good ResearchBlogging account, scienceblogs.com/principles/2012/05/… (to add to the motls.blogspot.com/2012/03/… link on the question physics.stackexchange.com/questions/22717/…) $\endgroup$
    – Peter Morgan
    May 6, 2012 at 16:27
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    $\begingroup$ There is more to it, which is that if Victor is at time-like separation from Alice and Bob's simultaneous detector events, he can make his choice based not only on the detector events, but also on the instrument settings that were used. However, an individual pair of simultaneous events (and the corresponding measurement settings) do not tell us, e.g., whether the Bell inequalities are violated. The violation of Bell inequalities is a property of a recorded sequence of simultaneously occurring events and the corresponding measurement settings, not of individual pairs of simultaneous events. $\endgroup$
    – Peter Morgan
    May 6, 2012 at 16:53
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    $\begingroup$ I strongly suspect that the answer has to do with the fact that you can't tell whether two experimental outcomes are correlated unless you do the experiment many times. When Alice and Bob make their measurements, their detectors either fire or they don't. It probably works out that the information you get from a single trial isn't enough to tell whether they're correlated, making your paradox-inducing version of the experiment impossible. If this idea is correct then fleshing it out properly will require reading the article - I'll do so at some point if I have time. $\endgroup$
    – N. Virgo
    May 6, 2012 at 17:43

1 Answer 1

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It turns out that Asher Peres' original theoretical paper on delayed choice entanglement swapping is short and quite readable. It sets out the idea behind the experimental setup without getting distracted by practicalities.

Basically the idea is that, as the Ars Technica post says, Alice and Bob each make their choice of measurement on one of the two photons the each have, and send the other to Eve. (It seems that Ma et al. renamed Eve to Victor - don't ask me why.) Eve then makes her choice of measurement on the two particles she receives.

This is then repeated many times. Alice, Bob and Eve all record which measurement they choose to make on each trial, as well as its result. Alice and Bob will each have a list of completely random measurement outcomes (each measurement produces a 0 or a 1 output with equal probability), which are not correlated in any way.

However, Eve also has a list of which measurements she made and what the outcomes were. What she does next is to sort the data from Alice and Bob's trials into four subsets, according to both which measurement she decided to make on that trial and what the result was. It then turns out that, according to the formalism of quantum mechanics, each of these four subsets will be correlated in exactly the same way as if Alice and Bob had been measuring entangled particles. This is what Ma et al. have confirmed experimentally.

The important thing is that the results of Eve's measurements are needed in order to sort Alice and Bob's results into subsets. This means that you don't have any information about whether the results from any given trial are correlated until after Eve has made her measurement, so Eve cannot cause a paradox by making a different decision based on information about the correlations.

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