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Spin and Measurement
Quantum TeleportationWhen I was writing about about teleportation, I wanted to explain exactly where quantum teleportation fit in, but the explanation got too long, so I moved it here.
Teleportation, for present purposes, is a process in which an object is scanned in one location and reconstructed in another. In other words, the object is considered to be nothing more than a particular arrangement of constituent parts, and teleportation is the process of determining and recreating that arrangement.
For macroscopic objects, teleportation is practically impossible. Any such object contains a tremendous number of atoms, and for each of them, we'd need to know what kind of atom it is, and what its position and momentum are … not to mention the fact that the atoms themselves have internal structure.
What about microscopic objects? Well, as long as there are two or more atoms, teleportation is still problematic. It's true we'd only need to know a few things, but we'd need to know them to arbitrary precision, all at the same instant. But, if there's only one atom, or, rather, only one constituent, then things get interesting.
See, the thing is, these positions and momenta I've been talking about are all relative to the center of mass of the object. The overall position has to change, otherwise what's the point, and the overall momentum has to change, too, so that the object arrives at rest. So, for an object that has only a single constituent, we don't need to know any numbers at all! All we need to do is find another similar constituent, and we can just declare that the object has been teleported!
(Or, as I mentioned in Physical Objects, we can declare that the constituents are instances of a single Platonic object, so that the object doesn't teleport, but rather exists simultaneously in multiple locations.)
Actually, there is one important thing I'm leaving out. Elementary particles, which are the constituent parts we're talking about, have spin, so if we want to say we've teleported one, we need to make sure that the spin state is reproduced.
For some particles, such as electrons, we can cheat. The spin state of an electron is like a little arrow pointing in some direction, so we can obtain any state from any other by applying a rotation. (OK, the spin state doesn't exactly point, and it has a phase as well as a direction, but the conclusion is still valid.) So, if we don't mind having a “teleporter” that doesn't preserve orientation, we can still just declare electrons to be teleported.
For other particles, such as photons, cheating doesn't work. The spin state of a photon is its polarization, and, as it happens, it's simply not possible to obtain any polarization from any other by applying a rotation. A photon with right-circular polarization, for example, always remains a photon with right-circular polarization, no matter how much you rotate it.
So, if we want to teleport a photon, or don't want to cheat, we need to actually do some work, and find a way to reproduce the spin state.
Unfortunately, we are immediately faced with a huge difficulty. According to quantum mechanics, whenever a measurement is performed on an object, the state of the object changes into one of just a few in which the property being measured is well-defined. There's no way to go back and measure all the other properties of the original state, so there's no way to ever obtain complete information, and without complete information, the state can't be reproduced, therefore, teleportation is impossible.
This, however, is where quantum teleportation comes in. A few years ago, some clever folks realized there was a flaw in the argument: you don't actually need to obtain the information in order to transfer it. You could, for example, take the object, put it in a box, and mail it somewhere, and voila, it would be transferred there. Of course that, by itself, wouldn't have caused much excitement, but they also realized that if you arranged things correctly, you could use Einstein's famous “spooky actions at a distance” to obtain exactly one bit of information and at the same time transfer the rest of the information somewhere else. Then you could send the last bit via conventional means and combine it with the rest to reproduce the original state.
That's the basic idea; for more detail see, for example, Quantum Teleportation.
What does it all mean? On the one hand, quantum teleportation is a real process, well described by the name “teleportation”; on the other hand, it applies only to elementary particles. As far as macroscopic objects are concerned, all it does is lift away the theoretical impossibility suggested by quantum mechanics to reveal the same old practical impossibility underneath.
o September (2002)
@ February (2003)