Disclaimer: IANA physicist, and IANA mathematician
Experiments have provided strong evidence to support the idea of "entangled particles," but I think there must be a limit to the distance...
"...two entangled systems appear to interact across large spatial separations..."or the Special Theory of Relativity must break down.
Here's where I see them as mutually exclusive:
Take the famous spaceship example for relativity... A spaceship has a clock synchronized to a clock on Earth. The ship leaves Earth and travels for awhile at or near the speed of light, turns around, and returns to Earth... the clocks will read differently, with more time having passed on Earth than on the ship.
Now add to that example a pair of entangled particles. Separate them and keep one on the Earth while one goes on the ship. For this mental exercise, it doesn't matter that the particles can't be monitored without changing the states (they can't transmit information)... while on the trip, if the action at a distance has no limit, then if one changes state a million times, the other will change state a million times. If they change state the same number of times, then time is not relative between Earth and the ship.
If anyone sees a hole in this attempt to apply logic, I would very much appreciate you straightening me out via a comment to this post.