This is unrelated to quantum in any way. The limit of accuracy to perfection is smooth. That is, it makes sense to 1-box even for a 51% accurate predictor, and the expected utility goes up with accuracy, reaching its maximum for a perfect predictor.
according to one of our most accepted theories these days (quantum mechanics) the inherent randomness of our universe
And yet I'm able to perfectly predict that 2+2 is 4. The agents being predicted are abstractions, like behavior of computer programs determined by source code. It doesn't matter for reasoning about an abstraction that its instances of practical importance get to run within physics.
In most formulations I've seen the word "you" is used, implying that the reader is the agent being predicted. I've never seen them limited to trivial agents that a human-level intelligence can predict.
It's an open question whether it's possible for Omega to exist, who can predict a truly complex intelligence, which is itself modeling the universe including itself.
My understanding is that perfect predictor decision-thought-experiments are just simplified versions of "pretty good predictor thought experiments." Like, if you. know that Omega is 90% accurate, it's probably still better to one-box.
What's even the point of making decision theories for dealing with perfect predictors (newcomb's paradox) when we know that according to one of our most accepted theories these days (quantum mechanics) the inherent randomness of our universe does not allow perfect prediction even with unlimited current and past knowledge?