Entanglement Happens

There have been a bunch of stories recently talking about quantum effects at room temperature-- one, about coherent transport in photosynthesis , even escaped the science blogosphere. They've mostly said similar things, but Thursday's ArxivBlog entry had a particular description of a paper about entanglement effects that is worth unpacking:

Entanglement is a strange and fragile thing. Sneeze and it vanishes. The problem is that entanglement is destroyed by any interaction with the environment and these interactions are hard to prevent. So physicists have only ever been able to study and exploit entanglement in systems that do not interact easily with the environment, such as photons, or at temperatures close to absolute zero where the environment becomes more benign.

In fact, physicists believe that there is a fundamental limit to the thermal energies at which entanglement can be usefully exploited. And this limit is tiny, comparable to very lowest temperatures.

(That's cut-and-pasted-- there are obviously words missing from the last sentence, but I don't know what they are.)

Is this saying that entanglement does not happen at higher temperatures? No, it's not. What's going on here is a little subtle, so it's worth talking a bit about (even though I know this will invite comments from crazy people).

The generic sort of entanglement experiment looks like this:


In the center, you have a black box that emits photons whose polarizations are entangled. That is, the two photons are guaranteed to have the same polarization, when they're measured, but that polarization is equally likely to be either horizontal or vertical. Those photons travel out from the box to two detectors consisting of a polarizing beamsplitter that sends horizontally polarized photons to one detector (where a photon is registered as a 1), and vertically polarized photons to another (registered as a 0).

If the photons are entangled, when you look back over the results of many repetitions of the experiment, you will always find pairs of identical numbers. If one detector gets a 0, the other also gets a 0 (I'll call this "00" to keep things compact); if the one gets a 1, the other also gets a 1 ("11"). When you look over a long list of results of the experiment, you'll see roughly equal numbers of "00" and "11" results, but never a "10" or a "01" (assuming ideal detectors, etc.).

Of course, this has left out the possibility of interaction with the wider world, so let's think about what happens if we do something to one of those photons en route to the detector. Imagine that a tiny demon, bored with sorting hot and cold molecules comes along and sticks a polarization rotator in the path of one of the two photons, like this:


What happens then?

The effect of the rotator is to change the polarization of the photon, whatever it may be, by a fixed amount-- say, rotating it 45 degrees counter-clockwise. So, vertical polarization becomes "up and to the left" while horizontal polarization becomes "up and to the right."

The ultimate polarization of the photon is still entangled with the other photon, though, so when the photon on the left is measured, the photon on the right is instantly determined to be one of the two possible polarizations. If we get a "0" from the left detector, the polarization is up-and-to-the-left, while if we get a "1," it's up-and-to-the-right.

What does that mean for our detector on the right? Well, it's still aligned to call horizontal polarization "1" and vertical polarization "0," so we need to know what the probabilities of those two results are. A photon polarized at 45 degrees from the vertical is equally likely to be detected as horizontal or vertical, so you are equally likely to get either "10" or "11," assuming the photon on the left was a "1." If the photon on the left was a "0," you're equally likely to end up with either "01" or 00."

When you look down the list of experimental results for this experiment, you won't see any sign of entanglement. All four possible outcomes-- 00, 01, 10, 11-- will show up, in roughly equal numbers.

So, the demon has destroyed the entanglement, right? No. The entanglement is still there, it's just that we're doing the wrong experiment to see it. If a tiny little angel were to tell us that the demon was there with his rotator, we could compensate for it by rotating the detector on the right by 45 degrees.


In that case, we would get back to our original scenario: we would only see "11" and "00" results, never a 01 or 10. If we know the effect of the environmental interactions, we can get back the results that show entanglement.

What does this have to do with room temperature systems, compared to cryogenic ones?

Well, we don't have any microscopic demons running around, but there are a lot of things that can happen to entangle the states of two quantum particles. Photon polarizations are actually pretty robust, as these systems go, but even there, if you try to send the photons any appreciable distance, you need to take a good deal of care to make sure that they get to the detectors in the same state that they started. If you're dealing with things like atoms or ions, which have more ways to couple to the environment, the problem is even worse.

In the demon picture presented above, each of the possible interactions-- each atom or molecule in the path of a photon, or each field mode that an atom might couple to-- acts like its own little "demon," potentially changing the state of one of the particles. This doesn't destroy the entanglement, but it makes it very difficult to measure. If you're dealing with one demon who may or may not be messing up your photon polarization, you can find ways to get around that. If you're dealing with a million little "demons," or 1023 of them, it's pretty much hopeless. Which is why experiments looking for quantum entanglement generally work with very tightly controlled systems, in high-vacuum chambers, often cooled to extremely low temperatures.

That probably sounds like there's a bit of hedging going on, and you're right, there is. It's generally advisable to work at extremely low temperatures in entanglement experiments, because you know that will work. At higher temperatures, you have more interactions that can possibly mess up the system and obscure whatever entanglement you manage to create. It's fiendishly difficult to calculate exactly what will happen, though-- I called them demons for a reason-- so there's a little room for things to sneak through. It's possible that, for some relatively high-temperature systems, it's possible to observe quantum coherence and even entanglement, if things work out the right way.

What's the deal with the paper cited by axivblog, then? The authors of that paper are looking at a specific idealized scheme for preserving entanglement in spite of environmental interactions, using a particular form of "squeezing" to generate entanglement and maintain it even with relatively strong environmental interactions. Of course, the specific system they talk about, two trapped calcium ions, is the sort of thing where entanglement can be established fairly easily with cooling techniques, so it's not immediately clear why the proposed scheme is an improvement. It is, however, a system for which the interactions are relatively easy to define, so it's easy to calculate the effects they're looking for.

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What a shame. Not any "un-crazy people" were motivated yet to leave comments. (BTW, sometimes crazy people end up being right after all, at least "technically": http://scienceblogs.com/principles/2010/01/neil_bates_owes_me_160.php/#…
, whatever the implications are after that.) But quantum mechanics is "crazy" anyway, everyone knows that! Well, what does entanglement say about superpositions? Since it's a relationship between observed outcomes, it is not a comprehensible property of the wave function considered by itself. IOW, it is not like the traditional independent WF, a definite state of specific amplitudes in time and space which give chances of getting e.g. H or V polarization with any one measurement. We couldn't even represent the entangled state without implying that interaction picks out one possibility and discards another; and such that can be compared to the "selection" done when the entangled WF interacted elsewhere. In a world where "Schroedinger evolution" just went on and on without "collapses", what would the correlation even refer to? (There would always just be "both" H and V amplitudes going in both directions.)

This raises challenging questions about how MWI handles entanglement correlations. To be consistent with results, the splitting process (however imagined) has to ensure there is one "world" with say results 00 and another world with results 11 - it must coordinate the entanglements. Formally I guess it can do that, but consider the challenge of "imagining" it being properly grouped: suppose one detector D2 is much farther from the source than D1. Let's say I observe "1" in D1, in my split. If any kind of "realist", I'm not supposed to imagine that observation "immediately" and literally converts the second photon into H because that violates Lorentz invariance (relative simultaneity.) But when the 2nd photon reaches D2, it must be manifested as H also. So is it still "really" a separately unspecifiable wave function, but curiously with an ineluctable destiny (and how do we *now* represent it?)

But to some observers D2 would be reached first - and could occasion a "splitting" of a world by itself. In any case, each world needs to respectively keep the two sets 00 and 11 together somehow in light of all those relative conditions. (So it can't be that every separate observation just makes its own "world.")

I wonder, as a worse problem: how come the splitting of a photon in e.g. the first beamsplitter of an MZI doesn't create separate worlds, but the action of a second BS does multiply "worlds?" If the first one did we just wouldn't get the interference, no matter how many worlds there are (;-0) Maybe if we imagined a Kantian world of relations there would be no worries about "what really happens."

After Neil B's taunting about a dearth of comments, I feel compelled to write exactly the kind of jackass comments that were discussed a week or two ago when pointing out how many of the comments about QM miss the point of the target audience of these articles:

1) The example photons aren't shown to be entangled, only classically correlated!

2) I would be more excited if the demon should be entangling the particle with orthogonal states of the environment, no rotating it!

That kind of missing-the-point aside, I liked the example, and it gives a good feeling for why I can't do ion-based quantum computer experiments in my living room, but why we can have light-based interferometers (and quantum cryptography) working over kilometer distances, since photons can travel kilometers without bumping into anyone.

And I really liked the icon of the demon.

By Anonymous Coward (not verified) on 14 Feb 2010 #permalink

I feel compelled to write exactly the kind of jackass comments that were discussed a week or two ago when pointing out how many of the comments about QM miss the point of the target audience of these articles:

And just for completeness, I'll answer them.

1) The example photons aren't shown to be entangled, only classically correlated!

I was trying to keep this short(ish), so I didn't want to explain how to do Bell tests as well. You can easily extend this to measuring the polarizations at different angles, and show that they're really entangled, not just classically correlated.

2) I would be more excited if the demon should be entangling the particle with orthogonal states of the environment, no rotating it!

The demon is entangling the photon with orthogonal states of the environment. The environment states are |Demon> and |No-Demon>. The fact that it's entanglement with the environment is kind of hidden, I'll grant, but it's there.