Teleportation

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Sorgoth
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Teleportation

Post by Sorgoth » Thu Jun 17, 2004 9:00 pm

I don't understand it.

http://physicsweb.org/article/news/2/10/16/1
In quantum teleportation the quantum state of an object held by "Alice" is instantaneously sent to "Bob". The technique works by sending one half of an "entangled" light beam to Alice and the other to Bob. Alice measures the interaction of this beam with the beam she wants to teleport. She sends that information to Bob who uses it make an identical copy of the beam that Alice wanted to teleport. This original beam is lost in the progress.
Wouldn't sending the information to Bob defeat the entire point of teleporting in the first place? Or am I not understanding how this works?

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rwald
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Post by rwald » Thu Jun 17, 2004 11:16 pm

If I understand it, the information that Alice sends to Bob isn't enough to recreate the beam alone. The way in which that information interacts with the entangled pair is necessary to recreate the beam. Of course, I might be entirely wrong; I welcome any corrections.
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Post by Rat » Fri Jun 18, 2004 12:50 am

Alice and Bob? We are showing our age, aren't we?

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rwald
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Post by rwald » Fri Jun 18, 2004 12:52 am

Well, Alice and Bob are used often in cryptographic contexts, which is where I assume the researchers got them from. Or maybe from an analgous source.
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Post by Rat » Fri Jun 18, 2004 1:03 am

Okay, it seems that it's still current. My mistake. I guess I'm behind the times. This is nothing new.

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Post by Skeeve » Fri Jun 18, 2004 2:18 am

rwald wrote:Well, Alice and Bob are used often in cryptographic contexts, which is where I assume the researchers got them from. Or maybe from an analgous source.
Shouldn't it be Carol and Ted?
Then Skank Of America could start in...

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Post by exarch » Fri Jun 18, 2004 10:58 am

As long as it's not Will and Grace ...
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Tez
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Post by Tez » Sat Jun 19, 2004 10:46 am

rwald wrote:If I understand it, the information that Alice sends to Bob isn't enough to recreate the beam alone. The way in which that information interacts with the entangled pair is necessary to recreate the beam. Of course, I might be entirely wrong; I welcome any corrections.
Yah. (For teleporting a single two-level quantum system) the information "sent" from Alice to Bob is only two classical bits, which could be encoded in black and white ping-pong balls or green and red donkeys. Point is, the transmitted information has very little to do physically with the quantum state being teleported. Its not like we're breaking the object up into little bits and then transmitting those, as many sci-fi versions of teleportation intimate.

Also, as you mention, the quantum state is specified by two real numbers - which would certainly take a little more than those two classical bits to specify!

Finally, this is the first atomic teleportation, and it is better than previous versions, but we've been teleporting photonic states for a while now...

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Sorgoth
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Post by Sorgoth » Sun Jun 20, 2004 6:57 am

But...if the information is just being sent, why are they calling it teleportation? Am I missing the instant speed thing?

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rwald
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Post by rwald » Sun Jun 20, 2004 7:25 am

Sorgoth wrote:But...if the information is just being sent, why are they calling it teleportation? Am I missing the instant speed thing?
They're sending a small amout of information (the two standard bits, as Tex put it), and using that information along with the entangled atoms to recreate the beam of light at the receiving end. Now, in principle, you can only transmit the light as quickly as you can transmit the small bit of information. But the important thing is that the beam of light contains more "information" than was contained in theose two bits. How did the extra information traverse the distance? It was encoded in the entagled bits. How does that work? We don't exactly know, yet. The fact that entangled atom + small amount of information = beam of light will always give the same beam of light, regardless of how far apart the entangled atoms have become, is what's amazing.
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Tez
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Post by Tez » Sun Jun 20, 2004 10:38 am

Sorgoth wrote:But...if the information is just being sent, why are they calling it teleportation? Am I missing the instant speed thing?
What rbald said. (Tex?)

Also - much of the transfer IS instantaneous (all the "real" number paramters..), just not all of it. And the stuff that does need to be transmitted can be done so at the speed of light, whereas to transmit the atom itself you would have to do so at less than c. Another feature that makes it important is that the two classical bits - the ping pong balls e.g. - are extremely robust against transmission error. The states of quantum systems are not. This is why we are interested in getting teleportation working - it'll help us send fragile quantum information around a quantum computer easily for example.

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Sorgoth
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Post by Sorgoth » Sun Jun 20, 2004 4:37 pm

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?

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Tez
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Post by Tez » Sun Jun 20, 2004 5:44 pm

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.

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Sorgoth
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Post by Sorgoth » Sun Jun 20, 2004 6:50 pm

I GET IT! (Well, I get what it is, anyway. Which is good enough.)

Thanks Tez, the actual physical drawing helped quite a bit. (I learn by doing...) I understand now...

Wait...one more thing... How do YOU know how many times he has to rotate the paper (The second bit of information). Doesn't the dot have an equal chance of appearing in each quadrant on his paper? Oh! I just got it! The two bits of information ARE the quadrant! ...that is a very good example. I think I'm going to save that.

Okay, one more question: Since the particles (Or dots) are entangled, and what happens to one immediately happens to the other (not exact, I know), does this mean that information is being transmitted faster than light?

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Tez
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Post by Tez » Sun Jun 20, 2004 7:00 pm

Sorgoth wrote:I GET IT! (Well, I get what it is, anyway. Which is good enough.)

Thanks Tez, the actual physical drawing helped quite a bit. (I learn by doing...) I understand now...

Wait...one more thing... How do YOU know how many times he has to rotate the paper (The second bit of information). Doesn't the dot have an equal chance of appearing in each quadrant on his paper? Oh! I just got it! The two bits of information ARE the quadrant! ...that is a very good example. I think I'm going to save that.

Okay, one more question: Since the particles (Or dots) are entangled, and what happens to one immediately happens to the other (not exact, I know), does this mean that information is being transmitted faster than light?
Its a contentious issue re what is being "transmitted" FTL. Certainly the dot "appears" instantaneously on his paper. However, you cannot actually use this to communicate a bit to your friend instantaneously. The brief reason is roughly like this: Remember I said that a measurement on a single paper with a dot can only narrow it down to a region. Well, imagine it can narrow it down to one of the four quadrants (in fact I think it may only narrow it down to a pair of quadrants in reality, but whatever..). But now which quadrant the dot is in on his paper was chosen uncontrollably at random by your measurement. So your friend cannot get a FTL bit of info from you until he knows which rotation to apply to the paper. However, to know that he has to wait until you send him the two bits of info as to which of the four measurement outcomes you got - and of course those bits are going to come at speed c or slower...

Somehow quantum mechanics conspired to keep us from communicating FTL using entanglement...

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Post by Philip » Sun Jun 20, 2004 8:05 pm

Tez, may I copy your analogy and post it on another forum where somebody was asking about quantum teleportation?

It's a much better description than I can give.

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Tez
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Post by Tez » Mon Jun 21, 2004 7:05 am

Philip wrote:Tez, may I copy your analogy and post it on another forum where somebody was asking about quantum teleportation?

It's a much better description than I can give.
Sure (Its not JREF right?). At some point I think I'll add it to the miscellaneous section of my woefully out of date homepage at physicsnerd.com...

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Post by Philip » Mon Jun 21, 2004 8:37 am

Tez wrote:
Philip wrote:Tez, may I copy your analogy and post it on another forum where somebody was asking about quantum teleportation?

It's a much better description than I can give.
Sure (Its not JREF right?). At some point I think I'll add it to the miscellaneous section of my woefully out of date homepage at physicsnerd.com...
Thank you! No, it's not JREF; it's a small forum at an artsy site, ihaveasecret.com.

I'm a physics nerd in nuclear stucture, but I'm woefully inept at communicating. I received my Ph.D. in May.

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Sorgoth
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Post by Sorgoth » Mon Jun 21, 2004 7:44 pm

Ah, okay. That clears up some questions. The actual bits are bound by c.

Although...for the entanglement communication thing, explain why this scenario wouldn't work:

Okay, since the entanglement effect that you've done appears on the other particle, but you don't know exactly where, only one of four possibilities, couldn't you work out a system where 1 dot(Or entanglement effect)/second=a, 2/second=b, etc?

Or am I taking the paper experiment too literally, and there isn't any actual way to tell when the other entangled particle has been affected?

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Post by Tez » Tue Jun 22, 2004 9:02 am

Sorgoth wrote:Ah, okay. That clears up some questions. The actual bits are bound by c.

Although...for the entanglement communication thing, explain why this scenario wouldn't work:

Okay, since the entanglement effect that you've done appears on the other particle, but you don't know exactly where, only one of four possibilities, couldn't you work out a system where 1 dot(Or entanglement effect)/second=a, 2/second=b, etc?

Or am I taking the paper experiment too literally, and there isn't any actual way to tell when the other entangled particle has been affected?
Good point, I should have been a bit more careful. What actually happens is that the two entangled pieces of paper are not initially blank - they each have a dot on them. The crucial point is that this initial dot is completely randomly placed on the paper. After the measurement, the dot moves to one of the 4 positions as I described above.

SInce the initial dot is random, Bob cannot tell whether Alice has performed her measurement or not.