So we measure the particles and find that they are in inverse states. I assume there's a reason for this, but why are we sure that we're not just reading off a random number generator that's set from the same seed?
It's my sacred duty to keep repeating this fact until the whole internet knows. (It's even in the first sentence of the wikipedia page on quantum teleportation!)
If you don't get the classical information on the receiving end, any attempts to read the quantum state will garble the quantum transmission such that it'll be indistinguishable from random noise. Since those classical bits are limited by the speed of light, so is the overall transmission of the state.
I'm not prone to study too deeply because I've learned (apparently) very bad analogies or schemes for entanglement.
The receiver needs the two bits to choose which of four kinds of garbling occurred, so it can correct them with the appropriate post-processing (if necessary).
We aren't. In fact, according to the decoherence / many-world interpretation (and possibly others) that's exactly what happens.
When you "measure" (aka. entangle yourself with) one of the two photons, you end up (find yourself) in one of the infinitely many possible "worlds", in which both photons have a single, definite state (always the opposite of each other, in this setup.) It's as simple as that.
I keep recommending this sequence of blog posts as the best introduction to the topic:
2. There is no teleportation in the common man, sci-fi interpretation. In order to effect the information transferral we need three times as many particles as we're transferring the information of. Per particle whose state is to be tranferred, we need two entangled particles and a target particle. To translate that to the "teleporting a thing" case, if you were to teleport a cake, you'd need a cake, two (entangled) cake-equivalent mass collections, and a target "generic particle collection" to be turned into "your cake" after running the QT algorithm. It's only teleportation if you pretend that triplicate wasted-once-used mass isn't there, which we can't do: it's there, and this is QT, not 'regular' teleportation (ignoring the fact that there is no such thing outside of works of fiction =)
3. fair enough, I simplified that the wrong way.
https://en.wikipedia.org/wiki/Quantum_entanglement and https://en.wikipedia.org/wiki/Quantum_entanglement#Applicati... might work better as highlighting links here, although something like "Quantum Computation and Quantum Information" by Nielsen and Chuang would be a much better reference.
This is the part that I don't get - what's the physics mechanism behind this? It sounds very Schrodinger's cat.
It also sounds like a great way to tell if your information has been unknowingly accessed when it's travelling between two supposedly secure locations.
> It also sounds like a great way to tell if your information has been unknowingly accessed when it's travelling between two supposedly secure locations.
That's actually one of the currently possible applications of quantum mechanics to cryptography[1]. There are already multiple commercial implementations!
1. There is no duplication or copying of information, the original particle's state is destroyed. Copying is impossible when dealing with general quantum states[1]. (You may be thinking of measuring an entangled pair to randomly produce a stream of classical bits on each side that is the precise inverse of what is produced on the other side. This is not quantum teleportation.)
2. There is a very real notion of teleportation here, in that you take a particle with a quantum state A, and manipulate it in such a way that it stays where it is while causing a particle of the same type in a different place to be in precisely the state A, without actually moving the first particle to the second location. Yes, it's not likely to ever be used to beam anybody anywhere, but for photons it's very much like teleportation.
3. The two particles are not "literally the same", or even figuratively the same. The particles when measured will result in the other particle ending up in the opposite of the measured state, and this inversion persists even if we do operations that preserve the quantum state.
[1]: https://en.wikipedia.org/wiki/No-cloning_theorem