It's easier to think these as random number generators seeded with same value, taken six kilometers apart from each other, and then fetching values from them. No data is transmitted when fetching values from these.
That's basically the https://en.wikipedia.org/wiki/Hidden_variable_theory
The hidden variable theory makes it more complicated than it is.
If any type of interference or interaction happens to either of the particles after their initial mirror deflection, the correlation is gone. The complimentary nature of the measured values only applies when the particles remain untouched - thats why news articles a couple years ago were praising the ability to "entangle" particles for such a long distance/time. It's not easy to prevent all interaction.
The correlation is really just the undisturbed conservation of some quantity that was divided between the two particles.
In any "path" which splits a wave stream into x%/y% chance of trajectory/spin/polarization, etc, there will be an entanglement. All this means is that for every x% that went one way, y% went another, and the total is 100% ( conserved quantity.)
And you're describing entanglement in a misleading way. The most important part of entanglement is that you can't model it as two particles sharing secret data. When you touch one, you affect the output of the other. And this happens faster than light. It still looks random on each end, but once you combine the measurements you can see patterns.
My sense was that quantum physics basically makes sense if you go really small and have an understanding of how the particles interact. But entanglement is weird, because somehow there's also a mechanism for them to interact at distance?
(I know, I could try to look it up, but hopefully other people here have the same silly question)
As the GP said - to find out whether a particular change of state was random or a signal, one would need to compare readings from both.
Readings cannot be sent faster than the speed of light. Thus preserving causality.