As threatened in the previous post on new “quantum teleportation” results, here’s the first of three old articles on teleportation. This one discusses EPR states and “entanglement.” It’s somewhat linkrotted– in particular, the original news article is gone, but the explanation is still ok.

This dates from July of 2002, which is like 1840 in blog years.

Yet again, SciTech Daily provides me with weblog material, this time in the form of an oddball article in the Las Vegas City Life archives (how do they find this stuff? It never would’ve occurred to me to look there…). The article is mostly about the perils of futurism, but the new development which sparks the article, and caught my eye, is a “quantum teleportation” experiment done at the Australia National University (Important Caveat: There’s a tempting link in the upper left-hand corner of that page which promises a “Simple explanation of quantum teleportation.” This leads to a 2.5 MB PDF file, which may or may not be simple, but definitely takes a long goddamn time to download. There’s also a press release about the work, which is thoroughly uninformative, but does have a really cute chip-on-shoulder moment when it proclaims that the work “is ahead of similar efforts in Europe, Japan and the US; and demonstrates that truly world leading research is possible in Australia – if imagination, financial support and perseverance can be combined and nurtured.”).

(Actually, what really caught my eye about the article from Vegas was the suggestion that one goal of the experiment was “getting every researcher involved in the project wildly fucked by nerd groupies.” As one who has formally forsaken any involvement with nerd groupies (on advice of counsel, I should emphatically state that Kate is not a “nerd groupie”), I must say that I’m shocked– shocked!– at the idea that such work would be motivated by anything less than pure scientific curiosity. Well, mostly I’m shocked by the idea that they have nerd groupies in Australia (that’s what I get for going to grad school in Maryland– all they have in the D of C is political groupies), but I digress…).

The key idea in “quantum teleportation” is entanglement. I’ve mentioned this before, when talking about quantum computing, but it’s worth going over again. As with the quantum computing posts, this will take enough set-up (I need to explain the “EPR Paradox” to explain how “teleportation” works) that the actual material about “teleportation” (and maybe a bit of ranting) will appear tomorrow.

Say you’ve got two quantum objects– call them photons, to be concrete– each of which has two possible states– horizontally polarized or vertically polarized, for example. (Real photons can have polarizations at arbitrary angles, but you can thing of those as being a mixture of different amounts of horizontal and vertical polarization, so “H” and “V” are sufficient to describe the problem.) There are four possible states the two-photon system can be in: both horizontal (HH), both vertical (VV), or two possible states with one horizontal and one vertical (HV and VH). In general, until you make a measurement of the state, it’s in a superposition of all four possible states at once: HH + VV + HV + VH. This is sort of a weird state of affairs, but once you get past the problem with the superposition of states (no small trick), it’s a pretty mundane state. The states of the two photons are independent of one another– If you measure one of them to be vertical, you’re equally likely to find the other polarized vertically or horizontally. (You can think of it like a coin toss, if you like, with “H” being heads, and “V” being tails.)

However, imagine that you can do something to the system so that the states are no longer independent– in laser experiments, this is generally accomplished by using special crystals that spit out two photons when struck by laser light, with a very specific relationship between the polarizations of the outgoing photons. The details don’t really matter, what matters is that the end result is a state where the photon polarizations are correlated. If one is horizontal, the other is vertical, and vice versa. Until you make the measurement, the system is still in a superposition state, but now there are only two possible states in the superposition: HV + VH.

“Big deal,” you say, casually. It doesn’t sound that surprising, really, but it’s an exceedingly troublesome idea: Imagine taking the two photons, and shooting them off into space in opposite directions. Let them travel for, say, a year before you measure the state of either. At this point, they’re two light-years apart– something like twelve trillion miles. Now, imagine that you have some space alien friends with really good clocks sitting out there waiting for the two photons. Alien A measures one of the two exactly one year after it was sent out, and Alien B measures the other exactly one year and one nanosecond after it was sent out. If they get together afterwards, and compare results, they’ll find that their measurements are exactly and absolutely correlated– if A finds horizontal polarization, B will find vertical, and if A finds vertical, B will find horizontal. You can repeat the experiment a million times, and every time the two will have opposite polarizations.

“Big deal,” you say again. “That’s the way we set it up– when they left the crystal, one was vertical and the other was horizontal.” But that’s not how it works. According to quantum mechanics, the state is indeterminate until the measurement occurs. Until A measures the state of that first photon, the system is simultaneously in both HV and VH. The instant that A makes the measurement, though, the state of both photons is determined. Which means that, somehow, photon B has to know that photon A was just measured. But they’re two light years apart, and B was measured a nanosecond after A– a signal from A to B saying “I was measured! You’re horizontal!” would need to travel at 18,840,000,000,000,000,000,000,000 times the speed of light, which is ridiculous.

This bothered Albert Einstein to no end– after all, his claim to fame was proving that light speed was an absolute upper limit. The thought experiment described above (in slightly different form) was first posed as a paradox by Einstein, Boris Podolsky, and Nathan Rosen, as a counter-argument to disprove quantum mechanics. Einstein famously referred to the connection between the two particles as a “spooky interaction at a distance” (which is a great phrase, probably one honkin’ big word in German, and really ought to be appropriated as a description of Usenet newsgroups or weblogs…). This gedankenexperiment (another great German word) is known as the “EPR Paradox” in honor of the three authors of the original paper.

(One of the great ironies of the history of quantum mechanics is that Einstein’s work is one of the major pillars on which QM rests, and yet he himself found the theory philosophically distasteful, and spent his later years trying to find a replacement for it. He’s famously quoted as saying saying “I cannot believe that God would choose to play dice with the universe.” Only slightly less well known is this rebuttal from Pratchett and Gaiman’s Good Omens: “God does not play dice with the universe; He plays an ineffable game of his own devising, which might be compared, from the perspective of the players (i.e., everybody), to being involved in an obscure and complex version of poker in a pitch-dark room, with blank cards, for infinite stakes, with a Dealer who won’t tell you the rules, and who smiles all the time.”)

In order to get out of the EPR paradox, you need to do one of two things– either you need to sacrifice the indeterminacy of quantum mechanics, and develop a new theory in which the states of the individual particles are well defined through the whole experiment, even if they’re not known to the experimenters (such theories are called “hidden variables” theories, and that’s pretty much what Einstein was angling for); or, you have to sacrifice the whole idea of “locality,” the idea that particles are in specific places, and their properties are determined in those places– in essence, you have to say that the two photons are actually a single quantum system, even though they’re twelve trillion miles apart. Throwing away locality requires you to accept (paraphrasing an old textbook of mine) that the result of a random process occurring in one place can affect the result of another random process occurring at the same time in another place. Neither of these choices is particularly appealing, and it’s not immediately obvious how to distinguish between them.

In 1964, however, John Bell proposed an ingenious experiment which could distinguish between hidden-variables theories and non-local theories. In particular, he was able to show that the results of a certain set of measurements had to satisfy a certain inequality for any conceivable hidden-variable theory. If Bell’s Inequality is satisfied (or violated, depending on how you look at it), then there is no possible way to explain the results with a hidden-variables theory, and locality goes out the window. The first experimental tests of Bell’s Inequality were done by Alain Aspect and co-workers in 1982, and showed fairly conclusively that locality had to go. There are still people who argue that the experiments haven’t completely ruled out all counter-arguments, but most physicists regard this as a settled issue. Einstein was wrong, quantum mechanics holds up, and we live in a non-local world. (Explaining the details of Bell’s Inequality and the various debates about it is a topic for another post– if you’re interested, here’s a concise formal summary from a few years back, or you can Google on “Bell’s Inequality” and “EPR Paradox” for a wealth of other material).

This business of non-locality is another example of the deep and fundamental weirdness of quantum mechanics. It’s yet another pillar of the classical philosophical picture of science that had to be cast down to deal with a quantum world, and it doesn’t fall easily. We like the idea of locality– it makes life much simpler.

Happily, as with most of the other weird features of QM, non-locality and EPR states also turn out to open the way for interesting technological applications, particularly in what’s known as “quantum cryptography” (which I’ll talk about another time). These are also what make “quantum teleportation” work, but I’ve nattered on for rather a long time already, so we’ll save that for tomorrow, along with a bit of a rant about the over-selling of some experiments and the perils of science by press release.

Comments

  1. #1 PiGuy
    October 6, 2006

    Very cool desrciption of the EPR Paradox, locality, and indeterminate states.

  2. #2 Peter Fred
    January 10, 2007

    I have a question. Is not there a spooky “action at a distance” problem with the mass-based gravitational theories of Newton and Einstein? Maybe no one worries about this problem because they believe it is handled by either the (1)concept of the field or the (2)concept of the graviton which dark matter, the dark energy and the aether have never been detected in the laboratory?

    Here is a quote from Newton which indicates he is quite concerned about this action at a distance problem.

    “It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and effect other matter without mutual contact, as it must be….That gravity should be innate, inherent and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thing can ever fall into it. Gravity must be caused by agent acting constantly according to certain laws, but whether this agent be material of immaterial I have left to the consideration of my readers.” (emphasis mine)

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