Sorgoth wrote:Okay, so let me see if I understand (Forgive my lack of knowledge on how this all works... I am sadly uneducated. For now!): It's not really teleportation in the classic sense of the word, just mysterious, really efficient information sending (Beam of light with two particles).

So, while the particles themselves move at or less than the speed of light, they contain more than two bits of information.

...right?

Nope, that is a complete misunderstanding. Let me try and explain it properly. Please, read this through a couple of times if you dont get it, it took me some time and thought to compose it, and I believe it explains

*all* the essential features.

Take a square sheet of paper, and place a single dot anywhere on the paper. (I suggest actually doing it, it'll help later.)

Now to specify the location of that dot takes two real numbers - you can say something like "Its 3.27865... inches from the bottom left hand corner, and 4.734... inches up from the bottom left corner...". The location of this dot on the paper is very much like the "quantum state" of the atom.

Ok, imagine your friend, who is somewhere on the moon, has a blank piece of exactly the same sort of paper, and your task is to create a dot on his piece of paper at the exact same location that your dot is.

A cheating option is for you to simply mail your piece of paper to him. As I mentioned above, in practise this is hard because the mail service to the moon tends to corrupt the piece of paper in transit. And that'd hardly be teleportation right!

Ok, so another option is for you to call him up on the phone, and tell him where the dot is. There are several reasons this is unsatisfactory:

1. It requires sending an infinite amount of information. The actual physical location may well take an infinite string of numbers to specify (the 3.278652437234....).

2. You may not actually know the position of the dot! Above I asked you to put the dot on the paper, but circumstances may arise wherein someone

*else* gives you the piece of paper with a dot on it, your job is simply to make sure your friend ends up with a dot on his paper at the same location as the one on the paper youve been given, even though you do not, in fact, know the location of the dot.

Of course, you may well ask "Why can't I just measure the co-ordinates of the dot, and then call him up on the phone (with an infinitely long phone call) and tell him them?". The answer is part of the problem with quantum mechanical systems - when you make a measurement to determine the dot's location you necessarily cause a drastic and random disturbance to the dot's location on the paper. Not only that, but much more problematically, a single measurement

*cannot* actually give you the dot's location precisely anyway! The best it will do is narrow down the location of the dot to some region of the paper. If you wanted to narrow it down further, you'd need a second piece of paper that is identical to the first - i.e. with a dot placed in exactly the same location as the original paper (remember the orginal piece of paper has been disturbed and is useless now). But a measurement on this second piece of paper still won't nail down the dot's location exactly either - it'll just narrow down the region you know the dot to be in. So you need a third piece, identically prepared to the previous two.. But in the end you find you need an

*infinite* set of identically prepared papers, all with dots at exactly the same point, just to make the measurements which tell you the dot's position. And then you're going to have to spend infinitely long on the telephone telling your friend those co-ordinates!! And remember - you may very well have only

*one* copy of the paper and the person who gave it to you refuses to give you another, in which case the above strategy is completely moot anyway.. (I mention it because its an interesting example of quantum shmantum issues. Oh - and note that its provably impossible to photocopy the pieces of quantum paper)

Ok, so at this stage things seem pretty hopeless, short of the mailing option.

However, this is where quantum teleportation enters.

It turns out that you and your friend can have two pieces of blank paper which have a special correlation/connection (called "entanglement") between them. You now can take the paper with a dot on it to be teleported (that remember you may or may not know the location of, though its obviously more challenging if you don't know in light of the above discussion..) and interact it with your one of the blank pair of entangled papers. What happens is that a dot then instantaneously appears on your friends piece of blank paper! Better yet, 25% of the time it appears at EXACTLY the same location as the dot on the original piece of paper that you were given! So you've teleported your dot to him, and you can both head for the pub...

Hang on you say, what about the other 75% of the time? Well, in those cases the dot certainly appears on his piece of paper, but not quite in the right spot. To see what happens, divide your piece of paper into four squares - i.e. draw a line from the middle of each side to the side opposite. The initial dot you drew is in one of these four quadrants (sorry, my ascii skills arent up to drawing this!). Now, in that remaining 75% of the time, the dot appears on your friends' paper in exactly the right co-ordinates, but just in the wrong quadrant. That sounds like nonsense hey? By "exactly right" I mean exactly right with respect to the nearest corner of the page say. So if your dot was "3.27865... inches from the bottom left hand corner, and 4.734... inches up from the bottom left corner", then his dot may be "3.27865... inches across from the top right hand corner, and 4.734... inches down from the top right hand corner.."

Thus, in order for your friend to get the right state out of the teleportation, all he needs to do is to rotate his piece of paper - either once, twice or three times.

How does he know how many times he needs to rotate it? Well, it turns out that when you interacted the two pieces of paper you were holding, you actually did a measurement, and this measurement had four possible outcomes, each occurring with equal likelihood. The number of times he needs to rotate it (if at all) depends on which of these four outcomes you got. So you are going to have to send him two bits - 00,01,10,11 in order to tell him which rotation to do - the two ping-pong balls. However, that is very little communication cost, given all those problematic issues I've mentioned above, and these classical bits are

*much* more robustly sent.

I hope that gives you a sense of why teleportation is interesting. Its not exactly like the start trek version, which is provably impossible under quantum mechanics and special relativity, but its damn close and very useful.