I'm still not sold on this. I'm no quantum mechanics expert, but I do have a philosophy background, and it seems as if true omniscience -- possessing all possible knowledge -- seems like it should transcend this limitation.

Maybe I'm thinking about a form of omniscience that exists outside of time, in which case, of course an omniscient being would know what happens next, because they would know the future just as well as the past. (Example: Any omniscient being will know which photons will pass through a polarizing lens not based on prediction but based on already knowing the outcome.)

There are always hidden assumptions. The proof only applies up to half-omniscience being that know everything in the current and past of the universe, but not in the future.

As a less powerful entity, if you know all the result in the lab until now, you can consider an experiment made 1 hour ago and "predict" the outcome without breaking the laws of quantum mechanics.

Such an entity cannot exist.

Such a statement can't be proven.

Sure, just append "unless it turns out we were wrong" to every scientific and mathematical claim if it helps you feel better.

I only append that to philosophical claims and string theory.

"philosophical claims and string theory" sounds redundant to me

Interesting. I can point you to some very influential philosophers who argue that not only can such an entity exist, it necessarily exists.

Can you tell me more about why you think it can't?

Apparently many other influential philosophers disagree, so take that proof with a grain of salt. https://en.wikipedia.org/wiki/Trademark_argument#Criticisms_...