How do you detect a bomb so sensitive that a single photon will set it off - without blowing yourself up?
The prospect of being hanged, as Dr Johnson remarked, concentrates the mind wonderfully. And there's a similar incentive to understand quantum theory correctly if getting it wrong might prove fatal. Take bomb detecting. Suppose someone tells you there might be a bomb nearby, equipped with a trigger so sensitive that a single photon will set it off. Obviously, you would like to know if the bomb is there, but you can't just shine a light all around you to check: you'll discover the bomb only by blowing it up. Classically speaking, you're in an impossible dilemma, but once again the subtleties of quantum theory throw you a lifeline.
This puzzle was proposed in 1993 by Avshalom Elitzur and Lev Vaidman of Tel Aviv University in Israel who -- naturally enough -- had also come up with a clever, although imperfect answer. The key to their idea was a device called an interferometer which, in a manner of speaking, splits a photon in two and then puts it back together again.
The interferometer starts with a half-silvered mirror, which in classical terms reflects half the light that hits it and allows the other half through. Both reflected and transmitted light then travel along their separate paths, guided by normal, fully reflecting mirrors, and are made to recombine further down the line. Thinking about this in terms of quantum theory, it might seem that a single photon entering an interferometer must choose one path or the other, but that's true only if you have detectors along the way charting the photon's progress. If there are no detectors to provide further information, then any quantum description of the photon's whereabouts must contain two parts corresponding to the two paths the photon can take.
The interferometer that Elitzur and Vaidman enlisted for their imaginary bomb detector recombines the ghostly probabilities in such a way that the restored photon always emerges in a specific direction. But this is a delicate process. If anything happens to disturb either ghostly photon en route, the subtle recombination is spoilt, and there is then a fifty-fifty chance that the photon will emerge in either of two directions. Now take a supersensitive bomb, triggered by a single photon, and place it in one of the paths within the interferometer. What happens?
First the bad news: there's a 50 per cent chance the bomb will blow up. That's because the bomb is a photon detector, albeit an unusually sophisticated one, and any detector placed in one of the interferometer paths has a 50 per cent chance of registering a photon. Boom!
Then there's a 25 per cent chance the photon will come out in the usual direction, telling you nothing about the bomb's whereabouts. The really interesting possibility is the final one--the photon has a 25 per cent chance of emerging in the other direction. This can only happen if the bomb is inside the interferometer. Success. You've detected the bomb but since the photon came out unscathed, the bomb can't have gone off.
Loosely speaking, the bomb's presence alters the way the photon simultaneously explores both paths through the interferometer. This can allow the bomb to have an effect on the photon's travels without actually interacting with anything one would go so far as to call a real photon.
The trick has its drawbacks, clearly. There's a 1 in 2 chance the bomb will blow up, in which case, game over. And there's a 1 in 4 chance the photon will come out the usual way, and you won't know whether there's bomb there or not. If this happens, however, you simply send in another photon, and another after that if necessary. Keep plugging away until you either detect the bomb or blow it up, and your odds of finding it improve to 1 in 3.
It also helps to adjust the first partially silvered mirror so that light has only a very tiny chance of going down the path where the bomb might be. A single photon then has only a small probability of either detecting or exploding the bomb, and you have to send in lots of photons to get your result. But the chance of ultimately detecting the bomb without setting it off rises to 1 in 2. Practically speaking, though, not many bomb-disposal experts would be happy with a system that gave them only fifty-fifty odds of escaping alive.
Just a couple of years later, Anton Zeilinger and his team in Innsbruck -- the same people who performed the quantum teleportation trick -- came up with an almost foolproof version of the quantum bomb detector. Instead of sending in new photons, one after another, until they got a result, they devised a system that keeps the same lone photon circulating around and around.
Imagine a chamber where two facing walls are perfectly reflecting mirrors, so that a photon could bounce back and forth between them forever. Now divide the room in two with a slightly imperfect mirror, made so that it reflects almost all the light that hits it, but lets through a tiny amount -- one photon in a million, say. Next send a single photon into the chamber on the left-hand side of the central mirror.
As long as the photon goes undetected, we can't know whether it has been reflected or made it through. Gradually, it develops a ghostly double existence, split between the two halves of the chamber. At the outset, all of the photon is on the left-hand side; after one bounce, some small probability of the photon's presence has sneaked over to the right-hand side. With every additional bounce, the two "pieces" of the photon are divided again, but they also interact with each other when they meet in the middle. The upshot of all this to-ing and fro-ing is simple: after some time a photon that started out strictly in the left-hand side of the chamber will have leaked across until it is wholly in the right-hand side. And then it will start to trickle back to the left-hand side.
Now someone tells you there might be a supersensitive bomb in the right-hand side of the chamber. You introduce a photon into the left- hand side and let it bounce back and forth. After the requisite number of bounces, you check the left-hand side to see if the photon has vanished from there and leaked over to the right. If it has you know there's no bomb. But if the photon is still on the left - and here's the really clever part - you know the bomb is on the right. Cautionary note: there's a chance, while you're waiting to check the photon's whereabouts, that the bomb will go off. But the more reflective the central mirror is, the smaller the chance of an explosion. If the central mirror is almost but not quite perfect, you have to wait almost an infinite amount of time to complete the experiment, but the chance of detecting the bomb becomes almost 100 per cent, while the chance of setting it off drops almost to zero.
At first glance, it's hard to see why this setup should give a different result from the one that Elitzur and Vaidman originally proposed. In either case, each single passage of a photon gives a small chance of detecting the bomb, and you keep sending photons in until you've got a result. But there's a crucial difference, depending yet again on a quirk of quantum theory. In the Elitzur-Vaidman scenario, each photon contributes a small probability that the bomb will be detected, and a small chance it will explode. Successive photons reinforce these probabilities, at an equal rate, and in the end there's a fifty-fifty chance of either eventuality.
In the Austrian device too, each bounce of the photon has a small chance of setting off the bomb, and as long as it doesn't, the photon keeps bouncing back. But every time the photon strikes the central mirror and fails to explode the bomb, its probability of being in the left-hand side of the room stays at 100 per cent - as if it had never struck the mirror at all. When the photon bounces back for another attempt, it's as if all the previous attempts had never happened. Hence, no matter how many bounces have passed, the photon remains where it started - proving that there's a bomb on the other side.
The bomb trick depends crucially on the idea that an unobserved photon can "be" on both sides of the central mirror at once. This sort of thing happens so often in quantum mechanics that there's a name for it. It's called the uncertainty principle.