> [...] how sharing an entangled particle pair (...) is interestingly different than sharing a seed to an RNG
> They're apparently the same phenomenon
You're the one deciding that they're the same phenomenon, by choosing to only imagine using the entangled particle pair to seed a PRNG on each side using the same method.
The key thing to realize is that Alice and Bob have quantum mutual information, not classical, and that "quantum" here is not just technobabble but actually has meaningful consequences.
If Alice and Bob choose to destroy the quantum information and extract the same bit(s) of classical information from their respective halves of the entangled pair(s) before the game starts, then the quantum case has been reduced to the classical case and you can think of them as the same phenomenon. But if instead they keep the quantum information around past the start of the game and decide what to do with it based on the hand they're dealt, they can get a win rate that's impossible with only pre-shared classical information.
To be clear, I wasn't saying they were the same phenomenon. I was saying they're apparently the same phenomenon, even though I know they can't really be. My opinion was that it was the responsibility of the article to explain why these apparently identical phenomena are in fact distinct.
> They're apparently the same phenomenon
You're the one deciding that they're the same phenomenon, by choosing to only imagine using the entangled particle pair to seed a PRNG on each side using the same method.
The key thing to realize is that Alice and Bob have quantum mutual information, not classical, and that "quantum" here is not just technobabble but actually has meaningful consequences.
If Alice and Bob choose to destroy the quantum information and extract the same bit(s) of classical information from their respective halves of the entangled pair(s) before the game starts, then the quantum case has been reduced to the classical case and you can think of them as the same phenomenon. But if instead they keep the quantum information around past the start of the game and decide what to do with it based on the hand they're dealt, they can get a win rate that's impossible with only pre-shared classical information.