Enough slagging of beloved popularizers-- how about some hard-core physics. The second of three extremely cool papers published last week is this Nature Physics paper from the Zeilinger group in Vienna, producers of many awesome papers about quantum mechanics. Ordinarily, this would be a hard paper to write up, becase Nature Physics are utter bastards, but happily, it's freely available on the arxiv, and all comments and figures are based on that version.

**You're just obsessed with Zeilinger, aren't you? All right, what have they done this time?** The title is "Experimental delayed-choice entanglement swapping," and it's pretty much what it sounds like. They've demonstrated the ability to "swap" entanglement so as to create quantum correlations between two photons that have never been close to one another. And they've done this in a "delayed-choice" fashion, where the decision about whether to entangle them or not is made well after the two photons they're entangling have been detected.

**Oh, OK, that sounds-- Wait, what? They entangled them after detecting them?** Yep. The basic scheme is illustrated by this quasi-spacetime-diagram from the supplementary material:

The vertical axis represents time, moving into the future as you go up. They start with two pairs of entangled photons, which are sent into optical fibers. Two of these (one from each pair) go directly to detectors that record their polarizations roughly 35 ns after they were produced. The other two go into very long fibers, and are sent to a detector that either records the two original polarzations, or makes a joint measurement of the two together. If they measure the individual polarizations, the original pairs remain independent of one another, but if they make a joint measurement of the two, that entangles their states, meaning that the polarizations of the *other* two photons are now entangled with each other, and should be correlated.

Since these photons went into much longer fibers (104m vs. 7m), though, the entangling measurement is made *after* the two photons whose states are being entangled have had their polarizations measured-- about 520 ns after they were produced.

In keeping with the silly jargon of the field, the two photons that are detected immediately (Photons 1 and 4) go to detectors that are imagined to be held by people named "Alice" and "Bob." The two that are measured together to determine the entanglement (Photons 2 and 3) go to a third imaginary person named "Victor," and it's Victor's measurement that determines everything.

**OK, that's just weird. So, this means that the two photons either were or weren't entangled all along, right from when they left the original sources?** No, because the choice of whether to entangle them or not is made after the first photons have been detected.

**Wait, how does that work?** They use a clever fact about the behavior of photons hitting a beamsplitter, that allows them to control which type of measurement they make by rotating the polarization of the photons before they hit it. They have a fast polarization rotator (an "electro-optic modulator") which they connect to the output of a quantum random number generator (basically, something that looks at random noise from a light source, and converts it to a string of 1's and 0's), and that controls the measurement. A 0 from the random number generator does one measurement, and a 1 does the other. The numbers are generated at a rate that changes several times during the time that the photons are in the 100-m fibers, so the exact measurement being made isn't determined until they're already on the way.

**That's... Why would you do that?** It's an outgrowth of other experiments, where people make a delayed choice about whether to look for particle behavior (which path a photon took) or wave behavior (an interference pattern)-- see this one from five years ago, for example. This is a more complicated phenomenon, involving two particles at different locations, but it presents the same conundrum: Depending on your choice of entangling versus non-entangling ("separable") measurements, you would expect the two photons whose polarizations are measured first to be correlated in different ways: for a separable measurement, you expect the two photons to have definite linear polarizations, while for an entangling measurement, they will be in an entangled state, where both polarizations are undefined, but will be the same when measured.

If you repeat the measurement many times, for different settings of the polarization detector (that is, sometimes you measure horizontal vs. vertical linear polarizations, other times you measure left-hand vs. right-hand circular polarization), you can put all the numbers together and show that when the entangling measurement is made, you get results consistent with an entangled state (i.e., that violate Bell's inequality), and when the separable measurement is made, you get results consistent with definite linear polarization.

**So when they do this, what do they see?** Pretty much exactly what you expect. They display this as a bar graph, but it's just as easy to read out of a table:

They report two numbers for each of the possible results: a "state fidelity" which is a measure of how well the state they detect matches the state theory tells them to expect (you don't go far wrong if you think of it as the percentage of what they expect that they actually measured), and an "entanglement witness" value, which is negative if the two photons they're looking at are entangled.

The first row looks at the relationship between photons 2 and 3, and when Victor makes an entangling measurement of those two, you find that, as expected, they are entangled (the "witness" value is negative). When Victor makes a separable measurement, they're not entangled, as you expect.

The second row looks at the relationship between photons 1 and 4, and again, when Victor makes an entangling measurement, they are found to be entangled, and when Victor makes a separable measurement, they are not entangled. To drive home the point that this matches what is expected, cells corresponding to measurements that indicate entanglement are shaded orange.

**What are the third and fourth rows doing?** The third and fourth rows look at entanglement between photons 1 and 2 and photons 3 and 4. These are the original entangled pairs produced by the sources, and if Victor makes a separable measurement, they should still be entangled with each other. Which, again, is exactly what you see.

**And these are solid measurements?** Absolutely. If you want it in terms of standard deviations, the smallest entanglement witness value is negative by 4.7 times the uncertainty. Which wouldn't quite let you claim detection of a new particle, but is pretty darn good, and more than enough for the purposes of this kind of demonstration.

**OK. But... I'm sorry, I'm still hung up on the timing thing. If Victor's measurement is made after the other two, how can it affect the results that Alice and Bob get?** That's why this is a fun experiment-- because it's such a strange thing to think about-- it seems like you have causality running backwards in time, which is just bizarre.

**Yes, that's the problem. How does that make any sense at all?** It's one of those things that depends on how you choose to interpret the meaning of the quantum wavefunction. I always get the term mixed up, but Zeilinger inclines toward a view where the wavefunction is telling you something about our lack of information about the system, which I think is what Matt Leifer calls the "epistemic" view. In this sort of view, the weird results aren't all that alarming, because all you have are lists of measurement values. You don't see anything strange about them until you compare all four measurements, at which point Victor's results just let you sort Alice and Bob's measurements into groups that show a certain type of correlation. It doesn't make sense in this picture to worry about anything working backwards in time, because it's only an after-the-fact correlation that you observe.

The other big school of thought is what Matt Leifer calls the "ontic" view, where the wavefunction is a real physical thing, in some sense. I'm not sure there's a way out of the "backwards in time" problem there. I suspect this is where you just shrug your shoulders and say "quantum mechanics is freakin' weird." Somebody with a better sense of the field can correct me in comments if I've gotten this all backwards, though.

**Shouldn't you mention Many-Worlds, here?** Sigh. I suppose. In a Many-Worlds type picture, you would look at this as splitting the wavefunction off into branches that will eventually be found to have involved an entangling measurement and branches that will eventually be found to have involved a separable measurement. The state in a given branch has a definite value, but you don't know which branch you're in until the measurement results happen, at which point the state of your brain and your measuring apparatus have become entangled with the state of the photons, and you can only perceive one outcome.

**So, is this the end of the story?** Well, there's some room for improving this, certainly. For one thing, the state fidelities aren't that great-- only about 65%, due to technical reasons having to do with the way they make the photons. It might be possible to do better, though the obvious way to fix it would dramatically lower the count rate of an experiment that's already pretty slow and complicated.

The other thing that could be done to really make the weirdness of the result absolutely airtight would be to make sure that not only are the two sets of measurements separated in time, but that the locations of the measurements are "space-like separated," meaning that Alice and Bob are far enough apart, and far enough away from Victor, that there's no way for a signal to travel between them at the speed of light in the time between the determination of what measurement Victor will make and the time when Alice and Bob make their measurements. They don't have that arrangement in this particular experiment, because it's a pain in the ass to have all of the complicated systems required to make this work in different rooms, but in principle, there's no reason you couldn't do that.

As it is, a weaselly theorist favoring some sort of local hidden variable model could point to the small separation between the measurement locations and invoke some sort of cosmic conspiracy theory that would coordinate all the measurement outcomes without breaking relativity. At which point all the experimentalists in the room would pelt them with lab notebooks, but, you know, there's always one or two.

**Is this useful for anything? Beyond making my head hurt, that is?** Not that I know of. The point is basically just to keep poking at the areas where quantum mechanics predicts weird stuff will happen, and see if it does. Eventually, it's possible that one of these experiments will break down in some way that hints at a deeper or more complete theory, at which point everyone involved books a ticket to Stockholm to pick up their Nobel Prizes. Until then, though, it's just pushing the limits of where we can see quantum weirdness a little farther up the chain of complexity, proving yet again that the universe is a far weirder place than it appears.

Ma, X., Zotter, S., Kofler, J., Ursin, R., Jennewein, T., Brukner, ï¿½., & Zeilinger, A. (2012). Experimental delayed-choice entanglement swapping Nature Physics DOI: 10.1038/nphys2294

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I have a question to see if I'm understanding this correctly. When they make a joint measurement of the photons, there are two possible outcomes, right? Call them A and B. If you look at the subset that had result A, then it violates Bell's inequality. If you look at the subset that had result B, it also violates Bell's inequality. But if you look at both A and B together, there's no violation, right? There couldn't be, could there?

My feeling on the interpretation of these results, is that all the major QM interpretations make equivalent predictions. So if the experiment doesn't make sense under one interpretation, that just implies that your intuition about the interpretation is wrong.

Lovely experiment, but what's so silly about cryptology jargon?

Nice ResearchBlogging (and the previous one too).

At the end of the day, what causes these correlations (and fidelities and entanglement witness values) is some seriously kudos optical engineering, using optical components that are not exactly everyday objects for a dog. All of it is based on an enormous network of experiments that stretches back to Newton and beyond. I'm never sure whether it's cool or unsurprising that if you look for weird, you can find weird.

What about detection loophole? Can't some hidden variable theory simply claim the photons were either entangled or not all along but only entangled ones can be detected by entangling measurement?

I have a question to see if I'm understanding this correctly. When they make a joint measurement of the photons, there are two possible outcomes, right? Call them A and B. If you look at the subset that had result A, then it violates Bell's inequality. If you look at the subset that had result B, it also violates Bell's inequality. But if you look at both A and B together, there's no violation, right?

When they make the joint measurement, they get two possible results, both of which give photons that are entangled, just in two slightly different entangled states (they differ by a sign in one of the terms). Whichever subset they look at, they see correlations indicating entanglement between photons 1 and 4 (and also 2 and 3, which are the ones measured to do the entangling in the first place).

When they make the separable measurement, they again get two possible results (you can think of them as being either horizontal or vertical). Again, when they look at either subset, they see entanglement of photons 1 and 2 and photons 3 and 4, because they were originally created in an entangled state.

If they don't separate out the subsets corresponding to particular results, I suspect they don't see any Bell violation, because they're muddling together different groups of things, and that will tend to obscure the results. There might be some way of sorting the data that would still show correlations consistent with entanglement, though-- I'm not that clear on the exact measure they used.

What about detection loophole? Can't some hidden variable theory simply claim the photons were either entangled or not all along but only entangled ones can be detected by entangling measurement?

I'm not sure about that, since they only count data for cases where they detect all four photons. But there's probably an efficiency loophole in there somewhere. Again, people proposing it are likely to be pelted with lab notebooks.

Like a lot of quantum mechanical experiments the result is statistical. If you only had four photons you wouldn't see anything. In some ways it's an an artifact of the detector in a large statistical space. If you are looking for certain kinds of things, you are going to find them, but you can't look at everything.

For example, if Victor used the results of Alice and Bob's measurements to decide what he was measuring, he'd get a totally different result. If you used the first dozen A&B measurements to seed a pseudo-random number generator, you'd get yet another result.

I was always fond of thinking of the wave function as an object, but as I've followed more and more of these experiments, I've become more comfortable with the epistemic view. You can't know everything, and you have to choose what you are going to look for. This means you are going to see all kinds of apparently odd statistics.

P.S. I'd also say thank you for your blog and your writing posts like this one.

I don't see why this is surprising. The 'choice' of measurements isn't really a choice at all. It's random. That means there's no information in the system until you do the final correlation. I bet if they tried a setup where the type of measurement was predetermined, ie a real choice, the experiment would fail.

Naive question: Couldn't this be used for FTL communication? Let's say victor was really far away and changed his detector at known time intervals sufficient for alice and bob to determine with reasonable statistical certainty whether their photons were being entangled in each time block. With some error victor could communicate one bit per time block to far away alice and bob IN THE PAST.

Am I missing something obvious here? Either way thanks for the great write-up, these things are fun to think about.