## Tuesday, February 28, 2006

### Interaction-free measurements

I feel slightly dissatisfied with the way how the physics blogosphere described the recent media explosions about the so-called interaction-free measurements, especially because the blogosphere has made the question about the origin and originality of the ideas even more obscuring than the media. See news.google.com for the recent articles about quantum interrogation which is another name for these phenomena.

First of all, it is surprising that not a single of these media or blog articles mentioned the names of the physicists who actually invented quantum interrogation or interaction-free measurements. So who are they? Their names are

and the discovery was made in 1991 although the paper only appeared in a proper journal in 1993. The first experiments occured eleven years ago, in 1995, with the names of Paul Kwiat as well as Anton Zeilinger on the paper. Zeilinger, who is a leading Austrian experimenter in the field of quantum teleportation and related topics, had done some very closely related experiments already in 1994. The originally low efficiency of the interaction-free measurements was improved in 1999 in a paper by Kwiat et al., including Zeilinger.

The ancient philosopher thought that an arrow cannot really move because you can divide its path into infinitely many pieces, and because the total length of each piece is zero, Zeno thought that their sum must also be zero, and an inconsistency of mathematics is then a trivial corollary. Zeno was apparently unaware of the fact that "0 times infinity" can give a finite result.

He had also invented other paradoxes that are not relevant for the main point of this article - for example, in his "Achilles and the turtle" paradox, he showed that he thought that the sum of an infinitely long sequence of positive numbers (such as the geometric series in his case) had to diverge. Although these Greeks started science - the Euclidean geometry may be viewed as the oldest field of physics describing relative positions of perfectly solid bodies - truth to be said, their ignorance was often breathtaking. ;-)

Quantum Zeno effect

Let us jump by several millenia into Zeno's future. Consider a two-level system in quantum mechanics. For example, take an excited atom that is ready to decay into its ground state. Normally it takes some time T but if you keep on measuring the energy of the atom very frequently, you prevent the atom from jumping onto another level. Much like Zeno thought, if you divide the time into infinitely many pieces - and you insert measurement to each point - motion becomes impossible.

Another example is a particle that is able to tunnel through a barrier. Such a thing can occur in quantum mechanics but only if you give the particle enough freedom to be invisible for a while and re-appear on the other side. If you watch the particle permanently, the tunneling can't take place. Because of the same reason, the economy can't operate well under a Big Brother who is permanently watching i.e. in socialism.

OK, we know what the quantum Zeno's effect is about.

Interaction-free measurements

The improvement from the 1990s is that you may also want to look at a different place from the location of the particle, and you can still learn something about this location. The classic example is a light-sensitive bomb. Can you see (optically) whether the bomb is in the box while avoiding detonation? The answer is Yes, Elitzur and Vaidman argued. Click at the word "bomb" in this paragraph (don't be afraid, it will probably not explode) and you will learn how can you sometimes become sure that a bomb is able to explode without actually exploding it.

Sean Carroll has recently become famous for replacing an exploding bomb by a barking dog and the igniting photon by salami.

See this paper for a description how the Elitzur+Vaidman paper was written and why is the adjective "interaction-free" misleading (and dependent upon your interpretation of quantum mechanics) for these experiments. Lev Vaidman is by the way also one of the key players behind quantum teleportation. In 1999, the methods were improved by dividing the interference to many pieces, i.e. by using the quantum Zeno's effect mentioned above. See Kwiat's page for details.

At any rate, the ideas of Elitzur and Vaidman are primary, the infinitesimal "quantum Zeno" improvements in 1999 are an interesting addition to the original discovery, the experiments are rather straightforward, and the recent connections with quantum computing probably have more marketing than physics in it, especially because the concepts of "counterfactual computation" have also been known at least for 5 years.

A Christian graduate student could also use the same mechanism to experimentally reconstruct the events in which God initiated Jesus Christ without ever touching Mary. ;-)

If someone is convinced that the "counterfactual computation" can circumvent some problems in quantum computing and either reduce the error rate or decoherence, the most obvious way to use this insight is to build a working & large enough quantum computer. That would be really cool.

Similarity with Afshar

Incidentally, there is some remote similarity of these experiments with Afshar's experiment. Afshar also uses "negative information from scattering" because if you remember, he places the grid at the interference minima. His photons then interact with the grid much less than they would interact if the grid were placed at generic places (this is the counterpart of the bomb not exploding most of the time - or the dog not barking). Afshar then incorrectly interprets this setup as a 100% measurement of the wave properties by each photon, and he continues by saying that he can also measure 100% of the "which way" information - which verbally contradicts the complementarity principle.

I have argued that most photons in his setup cannot be argued to have measured the wave properties of light because they failed to interact and paint any interference pattern.

1. Excerpt: Lubos I think Dicke should be credited with the concept of IFM. Also Zenninger had some similar ideas but Dicke put it more clearly. Of course Elitzur and Vaidman should be credited for the clever thought experiment they used with the Mach-Zehnder interferometer. I agree that Afshar's experiment is of some resemblance. Actually I was a bit surprised that you didn't mention it when you discussed Afshar's misconception about QM (ok Unruh's response contains the essential physics of IFMs). But there is a crucial difference: Afshar used a coherent state as an input which splits in any multiport device so strictly speaking it is not an IFM. If he had used a nonclassical state (number or squeezed) his experiment might be very interesting and non-trivial.
P.S I'm glad that you also comment on quantum optical/computing advances not only high energy and strings which I find very difficult to follow (to say the least).

2. Lubos:

This so called "Interaction free measurement" is nothing new. And it was actually some mis conception of quantum mechanics, not the violation of the basic principle of QM that all measurements involve interactions.

Consider this: A chamber of pure hydrogen gas. This gas is perfectly transparent to visible light because there is simply no state transition in the hydrogen atoms which has the correct energy level to absorb the photons. Hence the photons pass right through without being absorbed or being emitted. So you can call it "interaction free".

However, although it is interaction free, it is still capable of providing some measurements. You can determine the density of the hydrogen gas in the chamber, for example. And this is done WITHOUT any photon being absorbed or emitted. How come? From classical optics we know any transparent media has an index of refraction of light. Because of that, the light passing through the gas is slightly slower than that pass through the vacuum. This time delay can be precisely measured using interference patterns and from that you can determine the density of the gas.

So that's a measurement. And there is no interaction since no photon is absorbed or emitted. How could it be possible?

The correct understanding is there IS interaction, but the interaction does NOT result in the photon being absorbed or emitted.

The same can be used to explain the bomb detection paradox. You get the measurement because there is indeed some interaction involved, even though you thought the photon by-passed the bomb. The interaction does not result in the photon being absorbed so the bomb is not triggered.