• Root (271)
  • digest (139)
    • debate (1)
    • economy (12)
    • education (5)
    • freedom (7)
    • freespeech (18)
    • idiots (9)
    • media (26)
    • music (1)
    • politics (29)
    • religion (1)
    • society (2)
    • stumbleupon (6)
    • tech-sci (3)
  • fun (22)
    • videos (7)
  • ideas (6)
    • epistemology (5)
  • meta (6)
  • misc (11)
  • news (36)
    • media (5)
    • politics (25)
  • personal (12)
    • florin (5)
    • lupo (6)
  • series (4)
    • complexity (1)
    • ponerology (3)
  • tech-sci (35)
    • comp (4)
    • medicine (28)
    • psychology (1)
    • quantum (1)

RSS feed

GPG/PGP pubkeys

How Quantum Teleportation Works

author: www-data

Scientists teleported information between ions a meter apart. Slashdot had it. And about every time when /. features a story about quantum teleportation, I spend about an hour or so to explain people how quantum teleportation works, and why it does still not mean that you can beam, or that it doesn't violate relativity. And so I did yesterday. Again.

So I figured I might aswell explain it here, once, and be done with it. Heck, I might even be able to push up the read statistics for this blog this way... Y'know, you never lived if you ain't got slashdotted ;) This is going to be a layman's guide -- those of you with some knowledge of quantum mechanics (undergrad level, for example), try this seminar handout (sorry, german only). As for the experts of you... you're not the intended audience, but enjoy the reading nonetheless :-)

Layman's Guide to Quantum Teleportation

Crash Course in Quantum Mechanics

A binary quantum mechanical system is in a linear superposition of states A and B. That is physicists' speak for saying that it is either 100% A, or 100% B, or anything in between; for example 30% A and 70% B.

However, while any linear superposition of states exists, you actually only ever see the pure states, i.e. either A or B. The very moment you measure (physicist speak for "look" :-), the system also "jumps" into that very pure state that you measured. The wave function of the system collapses to that very one pure state, that you measured.

The question now is: to which exactly of its componets does a mixed wave function collapse to, when observed/measured?

However, if you only have one copy, then it's like lottery: the outcome can be anything -- with some options being more likely than others... :)

Quantum Entanglement

One of the cooler things you can do in quantum mechanics that you cannot do in classical mechanics is to create an entangled pair -- i.e. you take two particles and perform a special kind of measurement on both of them. At the end of the measurement, the particles do not have any individual properties in terms of A and B, that is their quantum mechanical state cannot anymore be described as p1*A+p2*B. Instead, their A and B properties can be expressed only as terms of an entangled two-particle system. If you feel like you didn't quite understand it... it's not easy, you'd probably need to dive more into quantum mechanics than you wish to in order to grasp this. Just accept the thought: every particle's state (in terms of A and B) is not only unknown (as in un-observed), but is actually not defined. The particles have a state which cannot be described as a linear superposition of A and B. Their state only physically makes sense when described as a whole, not as separate entities. (Romantic, isn't it? :-p)

Two fully entangled particles are said to be in one of the four Bell states of maximum uncertainty. If either one particle should be measured, then the particles instantaneously dis-entangle. The wave function of the measured particle suddenly collapses to a pure single-particle state (either A or B, chances are 50-50). The wave function of the other particle collapses at the very same time to another pure state -- either the same or the exact opposite of the measured particle, again, depending on the Bell state they were in while whey were entangled.

This is the heart of the teleportation: that, when given two entangled particles, measuring one particle in one place will force another particle somewhere else to change it's state instantaneously. Spooky action at distance was whan Einstein called it, and, paradoxically, he laid the foundation of quantum teleportation while trying to actually disprove quantum mechanics by showing its absurdity...

Quantum Teleportation

So... now suppose you have a system at location #1, in an unknown configuration. "Unknown configuration" means that you don't actually know how much A and how much B there is in that system, i.e. x*A + y*B. You want that system to be at location #2. Intuitively, you have the following options:

1. pack your system into a bag and carry/mail it to #2
2. look exactly at your system at #1, call up a friend at #2, tell him what the system is made of and have him make one
3. teleport the system to #2

First option is the lamest, but will do quite well. But that we already knew, that's not why we're here :-)

Second option would be nice, but the problem is: it's not possible. Because of the wave function collapsing, there's no way for you to exactly determine the state of your system. Further, basic quantum mechanics says (the no cloning theorem) that no quantum mechanical system in an unknown state can be copied, so there goes any 1000-copies-statistics plan out the window...

The only thing we're left with (and, quite frankly, the geeks among us are probably pretty thrilled about it :) is to teleport the system in question from #1 to #2.

As it happens, you can accomplish this task using entangled particles.

What you do is you take a system of two entangled particles in one of the four Bell states of maximum uncertainty. You place one particle at location #1 (where Alice lives :), and another at location #2 (at Bob's). Now, Alice has 1 of the 2 entangled particles, and the original particle. Bob has the other entangled particle.

Quantum mechanics theory shows that if you now try to perform an entanglement measurement on the both particles that Alice has in her hands, i.e. the original source particle to be teleported and one of the two already entangled particles, then they ... entangle. too :-) That is, they fall into one of the four Bell states of maximum uncertainty. At the very same time, whatever quantum mechanical properties Alice's particle used to have, they are now gone. They have been instantaneously transfered to the other formerly enangled particle, that in Bob's hands. The original entanglement between Alice's and Bob's particle is also lost.

Again, in short: the very moment that you entangle Alice's particles (i.e. the original source and one of the already entangled particles), Bob's particle receives all the quantum mechanical information that the source previously had. Spookily, from all we know, this effect is not limited by distances. It has been proven to work over distances of several miles in no-time, and there's no theoretical limit to the spatial separation allowed.

The Classical Information

Although the actual quantum-mechanical information is transfered instantaneously, relativity is not violated. The information in Bob's newly created particle can not be of any use (yet), because of a tiny but important detail: although the information was spatially transfered, Bob does not yet have a 1:1 copy of Alice's particle. The particle that Bob now has is ... "twisted". (In physicist speak, the state of the particle is rotated about the A and/or B axis.) To get a grasp of what I mean, imagine that before teleportation, Alice had a particle x*A+y*B. After teleportation, Bob might have a particle x*A+y*B, but might aswell be something like y*A+x*B. Now you know that the numbers x and y mean the same in both systems -- you just don't know exactly how they would be twisted after the teleportation. There are 4 possibilities how they can be twisted, and all 4 are equally probable, there's nothing you can do to favor the one over the other.

Which of the four "twists" happend, however, can be told from Alice's remaining pair of entangled particles.

Remember?

I just told you that, after teleportation, while Bob has his shiny new (almost exact) copy, Alice is left with tho entangled particles in one of the four equally probable Bell states with maximum uncertainty. "Equally probable" here means that Alice cannot influence which of the Bell states she gets. However, she can find out during the entanglement measurement which one she got. The nice part is now that, depending on which Bell state Alice's particles have, Bob's particle has a corresponding "twist". That is, if Alice tells Bob what she's left with, Bob will automatically know how to "untwist" his particle.

To put it more shortly: the teleportation act itself leaves Bob with a "twisted" copy of the particle, and leaves Alice with the necessary information to "untwist" the particle.

Alice now has to transfer to Bob two bits of information in order for Bob to be able to really complete the teleportation process. And this is exactly where relativity kicks in again: Bob has to wait for Alice's information. This can (for what we know) be transfered only as fast as light.

Otherwise, should Bob choose to use (physicist speak: "observe") his particle without waiting for Alice's information, he has a 50-50 chance of collapsing his particle either into an A or a B wave function -- that is, regardless of the Alice's original particle, Bob can gain no information whatsoever about the teleported system other than he would have had anyway: maximum uncertainty.

Yes, nature's pretty much a bitch sometimes... :)

2009-01-24 22:48 | www-datarootshell.ro | [/tech-sci/quantum] | permanent link