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# Quantum Teleportation

saratdear
This is something our Physics teacher asked us to research and come. She only told 'teleportation', but I suppose she doesn't mean any sci-fi.

I did go through some websites, but most of it is over my head. Can anybody explain it to me in simple language? (Simple English Wikipedia doesn't have a page on it) I have studied Quantum mechanics in its basics, the uncertainty principle, and a little bit about the quantum mechanical model of the atom.
Bikerman
Try the following and if you still don't get it I'll have a bash.
http://www.its.caltech.edu/~qoptics/teleport.html
http://media.caltech.edu/press_releases/11935
http://www.physorg.com/news193551675.html
saratdear
Thanks for the links, Bikerman, but can you tell me what quantum entanglement means? Can we just take it that the photons are connected in a way?

EDIT: I didn't go through the pages..will do so tomorrow. Gotta head to bed.
Indi

i'm not sure how much i can simplify this, but... here goes.

Sometimes two particles get linked due to various processes - for example, sometimes when two particles get created together, one must be spin-up and the other must be spin-down. Now, until you measure, you don't know which of the two is up and which of the two is down... you just know one's up and one's down.

So you take one, and move it a thousand light-years away from the other one. Now you measure it... and you see it's spin-down. Immediately you know that the other one must be spin-up... just as if you'd measured it. But, that other particle is a thousand light-years away, so you got the information about what is going on a thousand light-years away immediately... not a thousand years later... so you got the information about what was going on all that distance away faster than the speed of light. That's what quantum entanglement is about.
Bikerman
I can't really add anything useful to that other than probably to say that classical theory tells us that no information can be transmitted at this 'instantaneous' rate between the two particles. So any communication between the two events would have to be at normal sub-light speed. You can argue that information is already being sent - otherwise how would the particle know which way to appear....you COULD say that....but I wouldn't..
saratdear

Thanks for the explanations you two. Let me try to explain what I could understand from this site and from what you said (and you could correct me ):

Two photons are in an entangled state. One of them is taken to a large distance away. A person at one end makes a measurement of the state of the particle. This information has to be transmitted to the other person, who makes the necessary transformation to the particle at this end. The particle is thus transformed to that state.

What I'm asking is, wouldn't the transmission of information take time? So its not instantaneous, is it?
Bikerman
NO!
No transmission. They could both agree to check at 1.00pm. Then whoever actually makes the measurement first doesn't matter and there is no communication. From the moment the first measurement is taken the other particle is the other case.
With photons we could measure spin - a quantum property. Possible spins for the photon are +1 and -1. From the moment the first photon is measured, and at that instant, the other photon then is the other spin. Now you may say - of course. Since they are opposite spin then the other photon was ALWAYS opposite spin. Yes true, but the bugger of it is that until the measurement NEITHER photon is one or the other.
Indi
 Bikerman wrote: Now you may say - of course. Since they are opposite spin then the other photon was ALWAYS opposite spin. Yes true, but the bugger of it is that until the measurement NEITHER photon is one or the other.

Yes, until they are measured, BOTH photons are BOTH spin 1 AND spin -1, and we can verify this experimentally.

That means that if you have one of the photons, you can tell whether or not the other photon has been measured. So let's say you sent a message including one photon, and you wanted to know whether someone had viewed the message. You just check your photon to see if it's still in superposition state, and if it is, no one has viewed the message. If your photon is not in superposition state, you know someone has viewed the message.

It gets better. Suppose Bikerman and i wanted to send a message to each other, and we wanted to know if anyone was intercepting and reading our messages. i could (theoretically) create an entangled photon pair, keep one half, and put the other half in the message to Bikerman. Bikerman then receives the message, but before he opens it, he checks the superposition state of the photon. If it's still indeterminate, he knows no one else has read the message. So now he contacts me and says "ok, measure the photon", and i do it, and he observes that now his photon goes into a single, determined spin (which is the opposite of the spin i have). Now Bikerman knows that the photon i have is definitely the partner of the one he has. So, the bottom line is that he now knows that the message has come from me unchanged, and unread.
Bikerman
And you can even go one step further and include entangled photons in the live coding or frame control. Then the moment anyone peeks the video immediately scambles.
saratdear
The reason I told transmission was because

 The site I referred to wrote: Alice makes an appropriate projective measurement (Bell measurement) of the unknown state together with her component of the shared entangled state. The result of this measurement is a random piece of classical information which Alice sends to Bob over their classical communication channel.

I was thinking classical communication channel meant regular methods (no matter how fast, its not instantaneous) or am I missing something here?
saratdear
Um...bump? Could anybody help me here? I don't get the transmission part in quantum entanglement.
Indi
What you're looking at is not just quantum teleportation in theory: you are looking at an actual apparatus that would actually accomplish it. There are a lot of things in that apparatus that are part of the transmission process, but have nothing to do with quantum teleportation per se (such as the squeezed lasers (they don't say whether they are phase or amplitude squeezed)).

That particular process requires a classical channel to accomplish. Quantum teleportation in general does not (but then the question is: how do you control which states get teleported, and to where - that's what that apparatus is about: controlling quantum teleportation).

All quantum teleportation is in theory is this:
• Place another particle at the location you want to teleport to.
• Entangle the two particles somehow.
• Measure the starting particle. This destroys the entanglement.
• The destination particle is now an exact copy of the particle at the moment of measurement. (The starting particle is now something else random: its original state is destroyed by the measurement.)

That apparatus is tricky. The first two steps are obvious (they're the two yellow clouds at the bottom left and right). But how they accomplish the entanglement is sneaky.

What they have is an already entangled pair (the two circle-plus things with "EPR" between them). Call that pair A1 and A2. Alice has A1 and Bob has A2.

Alice entangles IN with A1. She then measures the IN state PLUS A1. This measurement destroys the entanglement between IN and A1. She then sends that result to Bob via the classical channel.

Bob receives, via the classical channel, the measurement of A1 PLUS IN. Bob entangles OUT with A2, then copies the A1 PLUS IN state onto A2 PLUS OUT. But, since A1 and A2 are entangled, A1 = A2. A1 PLUS IN is the same as A2 PLUS IN. And if A2 PLUS OUT = A2 PLUS IN... that means OUT = IN. In other words, IN has been copied to OUT.

Voilà, teleportation.

Whatever quantum state IN was in has now been transferred to OUT. The quantum state of IN is, who knows?

Here's the process symbolically. Initially, the IN state is X, and the shared entangled pair is Y.

Alice has: X and Y
Bob has: ? and Y

Alice entangles X and Y to get the joint state XY. Bob entangles the OUT particle to his half of the entangled pair to get the joint state ?Y.

Alice has: XY
Bob has: ?Y

Alice measures the state of the entangled pair X and Y (which gives XY). This breaks the entanglement so that now the input particle is in a random state. The other particle's state is not a problem, because it is entangled with Bob's side.

Alice has: ? and Y, and the measurement XY
Bob has: ?Y

Alice sends Bob the value of XY over the classical channel.

Alice has: ? and Y
Bob has: ?Y, and the measurement XY

Bob copies the quantum state XY onto his pair, which breaks the entanglement.

Alice has: ? and Y
Bob has: X and Y

Voilà, teleportation.

Now, this is terribly simplified, because the actual process involves doing complex (as in complex, mathematically, not hard) superposition functions to really explain what is going on. But the bottom line is that you don't need a classical channel for quantum teleportation - you just need a classical channel for that particular process.
saratdear
 Indi wrote: Now, this is terribly simplified, because the actual process involves doing complex (as in complex, mathematically, not hard) superposition functions to really explain what is going on. But the bottom line is that you don't need a classical channel for quantum teleportation - you just need a classical channel for that particular process.

Thanks a lot for that! But what I'm asking is, wouldn't the whole process be limited by the speed of the classic communication channel? No matter how fast it is, Bob will have to wait to get the measurement XY. So it's not instantaneous.
Bikerman
saratdear wrote:
 Indi wrote: Now, this is terribly simplified, because the actual process involves doing complex (as in complex, mathematically, not hard) superposition functions to really explain what is going on. But the bottom line is that you don't need a classical channel for quantum teleportation - you just need a classical channel for that particular process.

Thanks a lot for that! But what I'm asking is, wouldn't the whole process be limited by the speed of the classic communication channel? No matter how fast it is, Bob will have to wait to get the measurement XY. So it's not instantaneous.
No. The teleportation could be instantaneous - just not using this method.
saratdear
 Bikerman wrote: No. The teleportation could be instantaneous - just not using this method.

That's news to me...I was thinking there was only this method.
toasterintheoven
saying two things happen concurrently must be terribly hard to measure when in quantum mechanics you deal with time to some extreme precisions.

I think I read somewhere about quantum projects where particles have been able to predetermine their whereabouts by fractions of a millisecond, or something like that
Now, I have a quantum headache! "Scotty, beam me up!"
I will have another go at this topic later.
Indi
 toasterintheoven wrote: saying two things happen concurrently must be terribly hard to measure when in quantum mechanics you deal with time to some extreme precisions. I think I read somewhere about quantum projects where particles have been able to predetermine their whereabouts by fractions of a millisecond, or something like that

There are tricks you can use to determine that two things are happening simultaneously without actually having to measure the time between the two things. For example: interference patterns.
tazone
the position of every particle must be sent from node 1 to node 2
also on node 1 we must destroy the original somehow or convert all mass to energy somehow
and on node 2 we must be able to build the body with the data from node 1 or revert the energy back into mass

it could be possible that through rapid light speed acceleration you can turn the mass into energy and with descelerascion back into mass
but this has never been proven
Indi
 tazone wrote: the position of every particle must be sent from node 1 to node 2 also on node 1 we must destroy the original somehow or convert all mass to energy somehow and on node 2 we must be able to build the body with the data from node 1 or revert the energy back into mass

No. That's Star Trek teleportation, not quantum teleportation.

 tazone wrote: it could be possible that through rapid light speed acceleration you can turn the mass into energy and with descelerascion back into mass but this has never been proven

This is all gibberish. We turn mass into energy and energy into mass all the time. It has nothing to do with acceleration and deceleration.
kelseymh
 saratdear wrote: Two photons are in an entangled state. One of them is taken to a large distance away. A person at one end makes a measurement of the state of the particle. This information has to be transmitted to the other person, who makes the necessary transformation to the particle at this end. The particle is thus transformed to that state. What I'm asking is, wouldn't the transmission of information take time? So its not instantaneous, is it?

Yes, I know this is eight months late, but scanning the thread I didn't see that you got an answer. The bottom line is that "transmission" is not necessary for the entanglement itself. It is only necessary if the two observers want to measure the entanglement.

As Indi described, you often create an entangled system ab initio (shoot a UV photon into a parametric down-conversion crystal, and get two entangled IR photons out). If you send these off to two separated observers, they can make their measurements "simultaneously", or close enough together in time that no signal can propagate between them. Do this over and over again, and let the observers collect nice long lists of their measurement results.

At this point, each observer just has what looks like a random sequence: sometimes they see a photon in one state, sometimes in another. No pattern, no special features.

But let them get together to compare the lists (this is where the "transmission through a classical channel" happens), and they will discover that, event by event, their results are correlated -- if A observed "vertically polarized", then B observed "horizontally polarized", or vice versa.

What's more, they will discover that their results are more correlated (by a large amount) than they would expect by chance, or even than they would expect if the photons were "pre-programmed" to be in particular states.

There is no "transmission" needed, or even possible, for these correlations to occur, but you do need transmission (or B hopping into his Cadillac Escalade and driving over to A's lab) in order to measure them.