Photon teleportation was first accomplished 5 years ago, and the june 17, 2004 issue of Nature magazine brings news about teleportation of a group of beryllium atoms. Therefore, teleportation is already reality, although we're still far from the (probably impossible) teleportation of human beings and macroscopico objects. The entanglement is the fondamental point in all quantum teleportation experiments. The mathematical functions describing each entangled particles' quantum state became completely linked, and this feature is used in the teleportation. Quantum teleporting may open the way to computers with speed a million or even a billion higher then ours.

Although human being or any macroscopic object teleportation is still a dream, quantum teleportation of photons (light particles) and of groups of atoms is already reality. Nature magazine latest issue (june 17, 2004) reports teleportation of a beryllium atoms

In movies presenting teleportation of either persons or objects, the object to be teleported is scanned in order to extract from it all necessary information to its reconstruction. After that this information is sent to a distant station, where it's used to rebuild the object. Sometimes matter is also teleported in the form of energy (in this case, the original has to disappear), other times local matter is used (in which case a copy is got; the original may or not be destroyed).

This kind of teleportation is made impossible by quantum mechanics. Heisenberg's uncertainty principle states that we may not know, with certainty, at the same time, a particle's position and its momentum, so that there would be an uncertainty in every measured position and momentum (and consequently, speed) of all electrons and atoms pertaining to the body that should be teleported. It's not possible to scan it and rebuild it using the information got in this way. The uncertainty principle is also valid for other pairs of quantities (not only position and speed); therefore, it's impossible to describe the complete quantum state of any object with the necessary precision to rebuild it.

To understand what happens, let's suppose that Alice has a photon in a state we call M, and she wants to transfer the information about M's polarization to her friend Bob, who will be far away at the moment of receiving this info. She doesn't want to send him the M photon itself, because its delicate quantum state could be altered in its way, or else because this polarization is part of a secret message, and Alice doesn't want it to be intercepted.

A photon is a particle of light. But light is also an electromagnetic wave. Therefore, it results from the oscillation of an electric field. To visualize this oscillation, imagine a rope vibrating with an end tied to a tree and the other one in your hand. You can make it vibrate paralel to the floor, or perpendicular to it. Actually, you my make it vibrate in any intermediary direction. The photn polarization is the direction of the electric field oscillation of the corresponding electromagnetic wave.

There is still another fundamental difficulty in order to send M's polarization. Alice can't simply measure the polarization and send it to Bob.

the state of a quamtum system, as a particle, for example, can't ever be completely known. As we've seen, the photon polarization can be anything between the vertical and horizontal directions. But when we measure it, we have a probability of 50% for vertical polarization, and 50% for the horizontal one. We never get the intermidiate polarizations in the measurement. But this was not the polarization before we measured it. The measurement itself altered the photon's quantum state. This is a fundamental point in Quantum Mechanics.

Hence, if Alice had measure M's polarization in order to send it to Bob, she would not only get the wrong polarization, but would also loose forever the possibility of knowing it. She has to find a way of sendint it, without having knowledeg of it.

A group of physicists overcame this problem in 1993 (to the particular case of photon teleportation) using a peculiar and fundamental caracterist of Quantum Mechanics named entanglement.

Entanglement is the basis of all quantum teleportation experiment. Focusing a photon beam over certain crystals, it is possible to separate photon beams which are entangled: each photon in one of those beams has a king of twin in the other one. We say they are entangled because the mathematical function (or wave function) which rules the behavior of one of them, is indissociable of the wave function which rules the other one. If one of those two photons interacts with a third one, its state, or the quantum information that caracterizes it will have repercussion over its twin, and therefore can be teleported.

Tiis means that it we measure a quantity of one of those particles, the same quantity will be automatically determined to the other particle, even a long time after the interaction, when both particles have a long distance separating them (provide that the entanglement had not been broken).

Let's suppose that Alice and Bob entangles two photons K and L so that their polarizations are equal. When measuring the polarization of photon K so that they learn if it is either verticle or horizontal, they 50% of probability of getting each of them. Photon L has exactly the same probabilities. But as they are entangled, when the measurement is done, both will have the same polarization, doesn't matter which of them will be measured before, how long will it take between the two measurements, at which distance they will be one from the other, if one is on Earth, and the other on Alpha-Centauri, etc., since the entanglement continues.

So, if Bob makes a measurment, and gets, let's say, vertical, he knows imediatly that Alice's photon, when measured, will also present vertical polarization.

If Alice wants to send Bob M's polarization (which they don't know), they'll need to entangle two photons, A and B, with the same polarization (which they'll not measure). Bob travels with his photon B and waits for Alice contact.

Alice entangles the photon M, which polarization she wants to send Bob, with Photon A, which she kept. In this way she gets the AM system, which is entangles to photon B. Next she measures the rapport between polarizations A and M, finding, for example, that A's polarization is perpendicular to M's, or parallel, or opposite, etc. (the individual polarizations are not measured). Measuring the relative position of the polarizations doesn't change them.

But, as photon B is entangled to the system AM, measuring the rapport between polarizations A and M, changes B's polarization. Moreover, with some algebra, its possible to determine which transformation must be applied to B so that its polarization is changed to M's polarization.

The most interesting point is that there's no way by which Bob could know that the measurement was already done, or which result did Alice get, unless she contacts him in a classic way to tell him her results. She has to pass him this information in a classical, conventional, but not quantum way. She might call, write an email or maybe fax him.

When Bob receives Alice's message, and applies the necessary transformation (it could be rotate B's polarization by 90^o, or leave it as it is, etc.), the photon B will have the same polarization as M. This is equivalent to teleporting M, because two photons with the same polarization are indistinguishable.

It is important to remind that the initial polarization of photon M was lost when it was entangled to A. Therefore, the original must be destroyed so that teleportation is achieved.

1) Zeilinger, Anton, Scientific American 2000, April (heavily used in the preparation of this text).
2) Kimble, J. e Van Enk, Nature, vol. 429, 737.

If you know a bit of Quantum Mechanics and its algebra, try those ones:

1) Einstein, Podolsky, Rosen, "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?" in Physical Review, volume 47, pag. 777 (1935).
2) Bennet et al., "Teleporting an Unkown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Cahnnels" in Physical Review Letters, vol. 70, pag.1895 (1993).