EchoVanguard wrote:Am I correct in understanding, then, that the only thing we're lacking for FTL communication is the ability to force a spin status on a particle?
Not even that. All we need to be able to do is, for any given particle, manage to set up a situation where the probability density functions on the receiver end given "sender does X" or "sender does something other than X" are different (which is what Frank's saying).
If you can force spin like you're suggesting, you can do this with a
single particle. You have 1:1 ratio of particle:bit.
If you can't force spin, but you can skew the results of spin, it takes
more particles. This is equivalent to being able to 'load' or 'not load' the receiver's coin at a distance. How many trials do you need to repeat before you can be certain enough you've correctly identified a loaded/unloaded coin? That's how many particles you need, so it's an N:1 ratio of particle:bit where N is however many trials you need to be comfortable with the error rate.
The ability to cause a particle to favor a result, by any amount, leads to information send. How much you can make it favor that result determines how many particles you need to have reliable transmission. The problem is, though, we can't cause this sort of favored result behavior. The current theories would suggest it's pretty much completely impossible: it's just not what quantum entanglement is.
FrankTrollman wrote:There are theoretical limits to such accuracy, but they are a lot higher than 50%.
And this is the part where it falls apart: can you predict the accuracy of a fair coin toss with higher than 50% accuracy? Because what we have shown is that, from the perspective of the receiver, he is always flipping a fair coin. If the sender measures the x-axis, the receiver flips a fair coin. If the sender measures the y-axis, the receiver flips a fair coin. If the sender doesn't measure at all, the receiver flips a fair coin.
The theoretical limit to the accuracy is 50%.
No higher. You can't predict what's happening on the far end any better than you can predict a fair coin toss. Note: this only applies to these types of quantum entanglement FTL systems, where they use measurements to communicate. There are other weird properties of entanglement people are exploring that work on slightly different bases, and are not at all disproven (as FTL communication). They aren't proven or experimentally demonstrated, but they aren't disproven either. I know a lot less about them.
Also, here's a crappy little
probability flow chart. (The variables are the same as in Grek's post: A = Alice observes positive, B = Bob measures at all.) The point is that Bob has the initial decision to send Alice down the P(B) or the P(~B) path, but once Alice is there, the probabilities Alice experiences are identical. I.e., P(A|B) = P(A|~B). Given that, how can Alice differentiate between B and ~B using A alone? That is impossible.