As a layperson, this is confusing. I thought you couldn't use entanglement for communication.

But if you have an entangled set X and Y, you can send your partner X while you keep Y. When you both look at X and Y, you will randomly get 0 or 1 while they get the opposite. While you can't control which you get, you can take advantage of the fact that only you and your partner know what these values are and it is guaranteed that nobody else knows what they are. You don't know how your partner has used this info until you get the conventional communication.

It's more complicated than that in reality but that's the principle of why it's useful.

I find it hard to grasp that there's no clever way to impart information over entanglement (without relying on classical messaging).

Is the state of entanglement fragile beyond our limits to record or alter? What about an ensemble of thousands of entangled particles - could we statistically sample some of them and force how they resolve?

What are the different properties that can be entangled? Angular momentum (spin, orbital) ...? Surely there's something we can clock and predict in the real world without requiring us to collapse the wave function to know what the state would be.

Randomness is fundamental to Quantum Mechanics as presently understood. If you can predict what quantum mechanics says is random, a whole host of consequences would ensue, starting with the breakdown of relativity.

You can nudge it in a couple ways, and you can statistically predict what may happen as a result. However, none of the ways you can do that result in communication, because you can't get around the way you can't choose the collapse. There is no way to communicate because you can't force the decision. If you do force the decision you break the entanglement.

I think this is one of the main errors people make on this matter; you hear "ah, if mine is "up" then theirs is "down" automatically, so surely if I set mine to 'up' then I can communicate with them?" But you don't get to "set" it. You have no choice in the matter. It just happens. In communication, you are ultimately communicating your choice to have a 0 or 1, and you can't communicate when you have no choices to make. In more classical terms, it'd be like me trying to send you a message with next week's lottery numbers. I can't; I have no control over those numbers. (Not a precise analogy since there's no "quantum" there, but I think the intuition is reasonable.)

"Measurement" causes collapse, correct? What is different about measuring the system in a way that forces how the system collapses versus a way that results in a random result?

Does the other entangled system yield random results if you try to force the collapse of its entangled sibling?

Can you describe some experimental setups? I'd like to know how we found that out.

The operation you are depending on to communicate doesn't exist.

It's a bit weird that you can choose to read UP/DOWN and your counterpart can read LEFT/RIGHT, or even a bit of both by reading at an angle, but you still can't move classical bits around that way, because you can't read "RIGHT". If you do fiddle with things to force a result, the fiddling will erase the entanglement, because under the hood, in math, those two things are basically equivalent statements. If you do force something, your forced result will have no bearing on what your counterpart gets; if you force "RIGHT" all that will happen is that your counterpart will still get a 50/50 in the LEFT/RIGHT basis. You didn't communicate anything.

Thanks so much for explaining this!

Still, I'm fairly sure there's at least a strong element of that being one of the primary uses for this. It is not intrinsically useful for moving classical bits around in the usual way, because we have that problem far better solved with conventional technology. (All this quantum stuff is slow compared to conventional communication, and only statistically reliable.)