Wouldn’t that imply FTL travel, at least for information?

Nonlocality basically means that the universe has a global RNG state. If you write some code that uses a global RNG and no other global variables, that code will still be "local" in the sense that functions cannot communicate information between each other using the RNG. But the outcomes of the functions might still be correlated in interesting ways (corresponding to entanglement).

No, non-locality simply means that effects happen at infinite speeds, not that they carry information.

For example, the Copenhagen interpretation of QM abandons both locality and realism - particles don't have definite states, and they also communicate at infinite speed (but in a way that can't carry information).

What does it mean to communicate without information? That genuinely sounds like an oxymoron.

Basically when you measure the state of two particles that are entangled, you find that their state is correlated in some way. For example, they may be entangled in such a way that their spins are the same. So if you measure one to be spin up (when measured along any axis), the other will also be spin up (when measured along the same axis). This happens regardless of the separation distance between the two particles. By carefully adjusting the axes along which you do your measurements, you can prove that the spins that you get are not predetermined (this is Bell's Theorem) and yet the particles are not communicating at the speed of light with each other either (the correlation remains even if you move the particles far apart and then do the measurements at the same time). Note that the actual spin value itself is random, and once you do the measurements the entanglement is broken, so you can't use this to transfer information faster than light. Hence what the parent poster means by "communication without information": each particle individually appears to be completely random, and yet when you compare them you see both particles are random _in the same way_ (or in the opposite way, particles can be anti-correlated too).

Thanks for the detailed answer. I guess the word “communication” threw me off.