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February 25, 2006

"God does not play dice with the universe."—Einstein "Albert, stop telling God what to do."—Bohr

The first experimental demonstration of quantum telecloning has been achieved by scientists at the University of Tokyo, the Japan Science and Technology Agency, and the University of York. The work is reported in the latest issue of Physical Review Letters. Telecloning combines cloning (or copying) with teleportation (i.e., disembodied transport)

The scientists have succeeded in making the first remote copies of beams of laser light, by combining quantum cloning with quantum teleportation into a single experimental step. Telecloning is more efficient than any combination of teleportation and local cloning because it relies on a new form of quantum entanglement -- multipartite entanglement.
"Quantum cryptographic protocols are so secure that they can not only discover tapping but also where and how much information is leaking out. Now, using telecloning, the identity and location of the eavesdropper can be concealed."
"It seems absolutely bizarre that counterfactual computation – using information that is counter to what must have actually happened – could find an answer without running the entire quantum computer," said Kwiat, a John Bardeen Professor of Electrical and Computer Engineering and Physics at Illinois. "But the nature of quantum interrogation makes this amazing feat possible."

Sometimes called interaction-free measurement, quantum interrogation is a technique that makes use of wave-particle duality (in this case, of photons) to search a region of space without actually entering that region of space.

Utilizing two coupled optical interferometers, nested within a third, Kwiat's team succeeded in counterfactually searching a four-element database using Grover's quantum search algorithm. "By placing our photon in a quantum superposition of running and not running the search algorithm, we obtained information about the answer even when the photon did not run the search algorithm," said graduate student Onur Hosten, lead author of the Nature paper. "We also showed theoretically how to obtain the answer without ever running the algorithm, by using a 'chained Zeno' effect."

Through clever use of beam splitters and both constructive and destructive interference, the researchers can put each photon in a superposition of taking two paths. Although a photon can occupy multiple places simultaneously, it can only make an actual appearance at one location. Its presence defines its path, and that can, in a very strange way, negate the need for the search algorithm to run.

And I ask again, what does that mean? Counterfactual computation? Interaction-free measurement? Chained Zeno effect? Whaaaaa?

The problem we wish to solve is how to optically detect the presence of something, but with no photons hitting it. The something could be many things, like a hand, a detector, an ultrasensitive piece of film, or a single atom. The two physicists who brought this topic to light in 1993, Elitzur and Vaidman (EV), considered a "superbomb", which, if it possessed the trigger/detonator element, would explode whenever hit by even a single photon. Some of the bombs possess the element, and some do not. (The former are the so-called "good" bombs, the latter are the "bad" bombs [please do not get on my case about which ones are really the good ones!]). The goal now is, given a supply of these bombs in sealed crates, find out which ones are the good bombs. (Also, we aren't allow to shake the crates, or otherwise risk disturbing the bombs.)

A detective limited to the realm of classical physics is in trouble. He can go into a completely darkened room, and pry off the lid of the crate. Then what? If there really is no light at all -- if no photons at all hit the trigger element -- then he gets no information. If, on the other hand, a single photon hits the element, well then by definition there is a loud explosion, and the detective knows that this was a good bomb. There seems to be no way to find the good bombs without always exploding them.

Enter quantum mechanics. The first solution to the problem posed by EV was also suggested by them. Namely, we can use the complementary wave-particle nature of light (or, indeed, of any quantum). Consider a Mach-Zehnder inteferometer, as shown below (left). It is composed of two perfect mirrors, and two 50-50 beam splitters. The upper and lower path lengths are set to be exactly equal. Under these conditions, there is complete destructive interference to the upper exit port -- any incident light always exits to the other port. Put differently, the probability is 0 for an incident photon to reach detector D_dark (hence the name), while the probability to reach detector D_light is 1 (ditto).

What happens when there is an object -- like the EV "superbomb" -- in one of the paths? (See above, right.) Now we can use our classical notions to understand the possibilities. There is a 50% chance that a photon will take the path containing the object, resulting in an explosion. But if this didn't happen (also 50% likely), then the photon must have taken the other path. At the second beam splitter, there is no longer interference, since there is only one way to get there. Therefore, the photon again makes a random choice. There is thus a 25% (= 0.5 x 0.5) chance that the photon goes to D_light; such a result gives no information (but also does not disturb the bomb), since it would have happened in the absence of the bomb. There is also a 25% chance that the photon is detected at D_dark. This never happened in the absence of the bomb -- whenever D_dark goes "click", we know that there was an object in the interferometer. And since we only send in a single photon, and it shows up at D_dark, it could not have interacted with the object in the interferometer (which object, even if it does not actually explode, is assumed to be completely non-transmitting).
We can in fact make the chance that the bomb blows up as small as we like (in principle, anyway). To understand the method, we need to consider another rather peculiar quantum mechanical phenomenon, the so-called "Quantum Zeno effect". First discussed in 1977 by Misra and Sudarshan, the QZE involves using repeated quantum measurements to inhibit the evolution of a quantum system. It relies on the quantum "projection postulate", which basically states that, for any measurement made on a quantum system, only certain answers are possible, and that the resulting quantum system is then in a state determined by the obtained results. This is easiest to understand with a particular example.

Consider a series of N polarization rotators, each of which rotates the polarization of light by an angle 90°/N. Therefore, after passing through all N of them, an initially horizontally-polarized photon will be vertically polarized. That is, it will have zero chance of passing through a horizontal polarizer and being detected.

However, if we intersperse a series of horizontal polarizers, one at each stage, then the outcome is quite different. For concreteness, consider the case of six cycles, so that the rotation angle at each stage is 15°. At the first polarizer, the photon has only a small chance of being absorbed --> 6.7% = sin2(15°). If it is not absorbed, then by the projection postulate, the photon must be horizontally polarized. The identical process happens at every stage. For the case of N=6, the chance that the photon was transmitted through all 6 polarizers is simply (cos2(15°))6, which is about 2/3. Note that without the interspersed polarizers, we never saw light at the detector. Hence, whenever we get a "click" at the detector, we know that the extra polarizers were inserted. Moreover, if we perform the experiment with a single photon input, and it shows up at the final detector, then of course it could not have been absorbed by any of the extra polarizers. And as we let the number of stages N become large (at the same time reducing the angle of polarization rotation accordingly), then the probability that the photon is absorbed vanishes -- the photon is always transmitted!
A few Saturdays ago, he had his heart set on bubbles. "We have a copy of C. V. Boys' book Soap Bubbles here on the ISS. It was published in 1911 and it's still a wonderful treatise on thin films. Every space station should have a copy," he laughs. "I wanted to see what thin films and bubbles might do in zero-g and felt it was a topic ripe for discovery."

Pettit prepared a solution of water, soap, and glycerin, and fashioned a bubble-wand from thin wire--a loop that could be re-sized from 3.5 cm (about 1.5 inches) to more than 15 cm (6 inches) in diameter. The experiment was ready. "But first," recalls Petit, "I decided to try a 'dry run' with water only, no soap."

He inserted the wand into a zero-g beaker and pulled it out again. "To my amazement," he says, "when the 2-inch loop was withdrawn, a thin film of water clung tenaciously to the loop. I've never before witnessed such a large-scale film of water."

To fully appreciate Pettit's discovery, just try the experiment in your own kitchen (on Earth). Fill a bowl with drinking water and fashion an adjustable loop of wire. No matter how hard you try, it's impossible to make water stretch across a loop wider than about 1 cm (0.4 inches). Any film you do make, furthermore, will be fragile. A gentle bump or breath of air will cause it to burst.

Pettit's films, on the other hand, were 5 to 11 cm (2 to 4 inches) in diameter and remarkably sturdy. He could shake them vigorously, blow on them ... even paint on them. "They were like little sheets of rubber," he marveled. "They could withstand all sorts of mechanical torture."

Pettit injected some tiny mica flakes into the film. This allowed him to observe otherwise-hidden flows and swirls. "I blew on the film using my own breath," says Pettit, and fascinating patterns emerged--some that looked like spiral galaxies. "These tracer particle patterns lasted for well over four hours."

Then it was time to paint. On one film, Pettit deposited four drops of food coloring: red, blue, green and yellow. Using a syringe with a thin tip (a canella), he shot a stream of air across the watery canvas, pushing the colors to and fro. One of his paintings looked like an eagle, others like abstract art.

"I wonder what someone like Matisse could do with this ephemeral medium?" wonders Pettit.

Posted by Jon Rubin at February 25, 2006 04:52 PM

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